The present invention relates to unsaturated carboxylic acid deriva¬ tives that can be used in the treatment of dysiipidaemia, atherosclerosis and diabetes, to pharmaceutical compositions comprising them, and to processes for the preparation of these compounds. The invention also relates to the use of these compounds for the preparation of medicaments for the treatment of dysiipidaemia, atherosclero¬ sis and diabetes. In most countries, cardiovascular disease remains one of the major dis- eases and the main cause of death. About one third of men develop a major cardiovascular disease before the age of 60, with women showing a lower risk (ratio of 1 to 10). With advancing years (after the age of 65, women become just as vulnerable to cardiovascular diseases as men), this disease increases even more in scale. Vascular diseases, such as coronary disease, strokes, restenosis and peripheral vascular disease remain the prime cause of death and handicap worldwide. Whereas the diet and lifestyle can accelerate the development of cardiovascular diseases, a genetic predisposition leading to dysiipidaemia is a significant factor in cardiovascular accidents and death. The development of atherosclerosis appears to be linked mainly to dysiipidaemia, which means abnormal levels of lipoproteins in the blood plasma. This dysfunction is particularly evident in coronary disease, diabetes and obesity. The concept intended to explain the development of atherosclerosis was mainly focused on the metabolism of cholesterol and on the metabolism of triglycerides. However, since the studies of Randle et al. (Lancet, (1963), 785- 789), a novel concept has been proposed: a glucose-fatty acid cycle or Randle cycle, which describes the regulation of the equilibrium between the metabolism of lipids in terms of triglycerides and cholesterol, and the oxy¬ genation of glucose. Following this concept, the inventors have developed a novel programme, the aim of which is to find novel compounds acting simul- taneously on lipid metabolism and glucose metabolism. Fibrates are well-known therapeutic agents with a mechanism of action via the "Peroxisome Proliferator Activated Receptors". These recep¬ tors are the main regulators of lipid metabolism in the liver (PPARα isoform). In the last 10 years, thiazolidinediones have been described as powerful hypoglycaemiant agents in man and animals. It has been reported that thia¬ zolidinediones are powerful selective activators of another isoform of PPARs: PPARY (Lehmann et al., J. Biol. Chem., (1995), 270, 12953-12956). The inventors have discovered a novel class of compounds that are powerful activators of the PPARα and PPARv isoforms. As a result of this activity, these compounds have a substantial hypolipidaemiant and hypogly¬ caemiant effect. More specifically, the invention relates to compounds derived from hex- enoic acid, of the formula (I) below:

in which: R1 is chosen from: • a (C6-Ci8)aryl radical optionally substituted by and/or optionally fused to a saturated or unsaturated monocyclic or polycyclic 5- to 8-membered nucleus optionally containing one or more hetero atoms chosen from O, N and S, the said nucleus itself being optionally substituted, and β

• a saturated, unsaturated or aromatic monocyclic 5- to 8-mem- bered heterocyclic radical, optionally substituted and containing one or more hetero atoms chosen from O, N and S; R2 and R3 each represent a hydrogen atom or together form a C3-C7 alkyiene chain; and R is chosen from a hydrogen atom and a C1-C10 alkyl radical; the optical isomers thereof, and also the pharmaceutically acceptable addition salts thereof with acids or bases. The acids that can be used to form the salts of the compounds of the formula (I) are mineral or organic acids. The resulting salts are, for example, the hydrochlorides, hydrobromides, sulfates, hydrogen sulfates, dihydrogen phosphates, citrates, maleates, fumarates, 2-naphthalenesulfonates and para-toluenesulfonates. The bases that can be used to form the salts of the compounds of the formula (I) are mineral or organic bases. The resulting salts are, for example, the salts formed with metals and especially alkali metals, alkaline- earth metals and transition metals (such as sodium, potassium, calcium, magnesium or aluminium), or with bases, for instance ammonia or secondary or tertiary amines (such as diethylamine, triethylamine, piperidine, piperazine or morpholine) or with basic amino acids, or with osamines (such as meglu¬ mine) or with amino alcohols (such as 3-aminobutanol and 2-aminoethanol). The invention especially covers the pharmaceutically acceptable salts, but also the salts that allow a suitable separation or crystallization of the com¬ pounds of the formula (I), such as the salts obtained with chiral amines. The invention also covers the stereoisomers of the compounds of the formula (I), and also mixtures of stereoisomers in all proportions. The compounds of the formula (I) above also include the prodrugs of these compounds. The term "prodrugs" means compounds which, once administered to the patient, are chemically and/or biologically converted by the live organism into compounds of the formula (I). According to the invention, the term "aryl radical" means a monocyclic or polycyclic carbocyclic aromatic group preferably containing from 6 to 18 car¬ bon atoms. Aryl radicals that may be mentioned include phenyl, naphthyl, anthryl and phenanthryl groups. The term "alkyl" means a linear or branched hydrocarbon-based chain containing from 1 to 10 carbon atoms and better still from 1 to 6 carbon atoms, for example from 1 to 4 carbon atoms. Examples of alkyl radicals are methyl, ethyl, propyl, isopropyl, butyl, isobutyl, t-butyl, pentyl, isopentyl, neopentyl, 2-methylbutyl, 1-ethylpropyl, hexyl, isohexyl, neohexyl, 1-methylpentyl, 3-methylpentyl, 1 ,1-dimethylbutyl, 1 ,3-di- methylbutyl, 1 -ethylbutyl, 1-methyl-1-ethylpropyl, heptyl, 1 -methylhexyl, 1-propyl- butyl, 4,4-dimethylpentyl, octyl, 1-methylheptyl, 2-methylhexyl, 5,5-dimethyl- hexyl, nonyl, decyl, 1-methylnonyl, 3,7-dimethyloctyl and 7,7-dimethyloctyl. The heterocyclic radicals are monocyclic or polycyclic radicals com- prising hetero atoms generally chosen from O, S and N, optionally in oxidized form (in the case of S and N). Preferably, at least one of the monocycles constituting the heterocycle comprises from 1 to 4 endocyclic hetero atoms and better still from 1 to 3 hetero atoms. According to the invention, the polycyclic heterocyclic nucleus consists of one or more monocycles, each of which is 5- to 8-membered. Examples of 5- to 8-membered monocyclic aromatic heterocyclic groups are heteroaryls, such as pyridine, furan, thiophene, pyrrole, imidazole, thiazole, isoxazole, isothiazole, furazane, pyridazine, pyrimidine, pyrazine, thiazines, oxazole, pyrazole, oxadiazole, triazole and thiadiazole. Preferred heteroaryl radicals that may be mentioned include pyridyl, pyrimidinyl, triazolyl, thiadiazolyl, oxazolyl, thiazolyl and thienyl radicals. The saturated or unsaturated heterocyclic radicals are heterocyclic groups bearing no unsaturation, or comprising one or more unsaturations derived from the aromatic heterocyclic groups defined above, respectively. When R2 and R3 together represent a C3-C7 alkylene chain, it is pre¬ ferred for R2, R3 and the carbons to which they are attached to form a cyclopentene or a cyclohexene. The aryl and heterocyclic radicals are optionally substituted by one or more of the following radicals G: trifluoromethyl; styryl; a halogen atom; a monocyclic, bicyclic or tricyclic aromatic heterocyclic radical comprising one or more hetero atoms chosen from O, N and S; and optionally substituted by one or more radicals T as defined below; a group Het-CO- in which Het represents an aromatic heterocyclic radi- cal as defined above optionally substituted by one or more radicals T; a Ci-C6 alkylenediyl chain; a C1-C6 alkylenedioxy chain; nitro; cyano; (Ci-CiO)alkyl; (C1- Cio)alkylcarbonyl; (Ci-Ci0)alkoxycarbonyi-A- in which A represents (CrC6)- alkylene, (C2-C6)alkenylene or a bond; (C3-Cio)cycloalkyl; trifluoromethoxy; di- (CrCio)alkylamino; (Ci-Cio)alkoxy(Ci-Cio)alkyl; (CrCi0)alkoxy; (C6-Ci8)aryl optionally substituted by one or more radicals T; (C6-Ci8)aryl(CrCi0)alkoxy- (CO)n- in which n is O or 1 and aryl is optionally substituted by one or more radi¬ cals T; (C6-Cis)aryloxy(CO)π- in which n is O or 1 and in which aryl is optionally substituted by one or more radicals T; (C6-Ci8)arylthio in which aryl is optionally substituted by one or more radicals T; (C6-Ci8)aryloxy(CrCio)alkyl(CO)n- in which n is O or 1 and in which aryl is optionally substituted by one or more radi¬ cals T; a saturated or unsaturated, monocyclic 5- to 8-membered heterocycle comprising one or more hetero atoms chosen from O1 N and S, optionally sub¬ stituted by one or more radicals T; (C6-Ci8)arylcarbonyl optionally substituted by one or more radicals T; (C6-Ci8)arylcarbonyl-B-(CO)n- in which n is O or 1 ; B represents (CrC6)alkylene or (C2-C6)alkenylene and aryl is optionally substi¬ tuted by one or more radicals T; (C6-Ci8)aryl-C-(CO)n- in which n is O or 1 , C represents (CrC6)alkylene or (C2-C6)alkenylene and aryl is optionally substi¬ tuted by one or more radicals T; (C6-Ci8)aryl fused to a saturated or unsaturated heterocycle as defined above, optionally substituted by one or more radicals T; (C2-Cio)alkynyl; T is chosen from a halogen atom; (C<rCis)aryl; (CrC6)alkyl; (C1- C6)alkoxy; (CrC6)alkoxy(C6-Ci8)aryl; nitro; carboxyl; (CrC6)aIkoxycarboxyl; and T may represent oxo in the case where it substitutes a saturated or unsaturated heterocycle; or T represents (Ci-C6)alkoxycarbonyl(CrC6)alkyl; or (Cr C6)alkylcarbonyl((Ci-C6)alkyl)n-, in which n is 0 or 1. The term "halogen atom" means a chlorine, bromine, iodine or fluorine atom. The monocyclic, bicyclic or tricyclic aromatic heterocyclic radicals prefera¬ bly comprise one or more hetero atoms generally chosen from O, S and N, optionally in oxidized form (in the case of S and N). Preferably, at least one of the monocycles constituting the heterocycle comprises from 1 to 4 endocyclic hetero atoms and better still from 1 to 3 hetero atoms. Preferably, the heterocycle consists of one or more monocycles, each of which is 5- to 8-membered. Examples of 5- to 8-membered monocyclic heteroaryls are especially pyridine, furan, thiophene, pyrrole, imidazole, thiazole, isoxazole, isothiazole, furazane, pyridazine, pyrimidine, pyrazine, thiazines, oxazole, pyrazole, oxadia- zole, triazole and thiadiazole. Examples of bicyclic heteroaryls in which each monocycles is 5- to 8- membered are chosen from indolizine, indole, isoindole, benzofuran, benzothio- phene, indazole, benzimidazole, benzothiazole, benzofurazane, benzothio- furazane, purine, quinoline, isoquinoline, cinnoline, phthalazine, quinazoline, quinoxaline, naphthyridines, pyrazolotriazine (such as pyrazolo-1,3,4-triazine), pyrazolopyrimidine and pteridine. Preferred heteroaryl radicals that may be mentioned include quinolyl, pyridyl, benzothiazolyl and triazolyl radicals. The tricyclic heteroaryls in which each monocycle is 5- to 8-membered are chosen, for example, from acridine, phenazine and carbazole. The term "alkylenediyl chain" means a divalent radical of linear or branched aliphatic hydrocarbon-based type derived from the alkyi groups defined above by stripping out a hydrogen atom. Preferred examples of alkylenediyl chains are chains -(CH2)R-, in which k represents an integer chosen from 2, 3, 4, 5 and 6 and >C(CH3)2 and -CH2-C(CHs)2-CH2- chains. The alkylenedioxy chains denote -O-Alk-0- chains, in which AIk represents linear or ij

branched alkylene, it being understood that alkylene is as defined above for alkylenediyl. Preferred meanings of -O-Alk-0- are, for example, -O-C(CH3)2-O Or -O-CH2-CH2-O-. The term "alkenylene" defines an unsaturated alkylene chain containing one or more ethylenic unsaturations, preferably one to three ethylenic unsatura- tions. Examples of alkylene chains are -CH=CH- Or-CH=CH-CH=CH-. Examples of C3-C10 cycloalkyl radicals are especially cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl, cyclooctyl or cyclodecyl radicals. Saturated or unsaturated, monocyclic 5- to 8-membered heterocycles are saturated, or unsaturated, derivatives of aromatic heterocycles. Mention may be made more particularly of morpholine, piperidine, thia- zolidine, oxazolidine, tetrahydrothienyl, tetrahydrofuryl, pyrrolidine, isoxazolidine, imidazolidine or pyrazolidine. The term "alkynyl" means an aliphatic hydrocarbon-based group con- taining one or more unsaturations of acetylenic type. A preferred example is

A first preferred group of compounds of the invention consists of compounds for which: R1 represents a (Cβ-Cisjaryl radical, preferably a (C6-C10)aryl, optionally substituted by and/or fused to a monocyclic carbocyclic or hetero¬ cyclic 5- to 8-membered nucleus containing from O to 4 hetero atoms chosen from O, N and S, which is itself optionally substituted; R2 and R3 each represent hydrogen or together form a C3-C7 alkylene chain; and R is chosen from a hydrogen atom and a C1-C10 alkyl radical. Another even more preferred group of compounds of the invention consists of compounds for which, when R1 represents a substituted (C6-C10)- aryl radical, the aryl nucleus is substituted by one or more of the radicals G chosen from: trifluoromethyl; a halogen atom; styryl; a monocyclic, bicyclic or tricyclic aromatic heterocyclic radical comprising one or more hetero atoms chosen from O, N and S; and optionally substituted by one or more radicals T as defined below; a group Het-CO-, in which Het represents an aromatic heterocyclic group as defined above, optionally substituted by one or more radicals T; a Ci-C6 alkylenediyl chain; a CrC6 alkylenedioxy chain; amino; nitro; cyano; (C1-C10)- alkyl radical; (C2-C-6)alkynyl radical; (CrC10)alkylcarbonyl radical; (C-i-Cio)alkoxy- carbonyl-A- radical, in which A represents (Ci-C6)alkylene, (C2-C6)alkenylene radical or a bond; (C3-Ci0)cycloalkyl radical; trifluoromethoxy radical; di(Ci-Cio)~ alkylamino radical; (Ci-Cio)alkoxy(Ci-Ci0)alkyl radical; (CrCio)alkoxy radical; (C6-Ci8)aryl radical optionally substituted by one or more radicals T; (C6-Ci8)- aryl(Ci-Cio)alkoxy-(CO)n- radical, in which n is 0 or 1 and in which aryl is optionally substituted by one or more radicals T; (C6~Ci8)aryloxy(CO)n- radical, in which n is 0 or 1 and in which aryl is optionally substituted by one or more radicals T; (C6-Ci8)aryloxy(CO)n-(C2-C6)alkenyl radical, in which n is 0 or 1 ; (C6-Ci s)arylthio radical, in which aryl is optionally substituted by one or more radicals T; (C6-Ci8)aryloxy(Ci-Cio)alkyl(CO)π-, in which n is 0 or 1 and in which aryl is optionally substituted by one or more radicals T; a saturated or unsatu¬ rated, monocyclic 5- to 8-membered heterocycle comprising one or more hetero atoms chosen from O, N and S, optionally substituted by one or more radicals T; (C6-Ci8)arylcarbonyl radical optionally substituted by one or more radicals T; (C6-Ciδ)arylcarbonyl-B-(CO)n- radical, in which n is O or 1 ; B represents (Ci-C6)- alkylene or (C2-C6)alkenylene and aryl is optionally substituted by one or more radicals T; (C6-Ci8)aryl-C-(CO)n- radical, in which n is O or 1, C represents (d-Ce)alkylene or (C2-C6)alkenylene and aryl is optionally substituted by one or more radicals T; (C6-Ci8)aryl radical fused to a saturated or unsaturated hetero- cycle as defined above, optionally substituted by one or more radicals T; (C2-Cio)alkynyl radical; T is chosen from a halogen atom; (C6-Ci8)aryl; (CrC6)- alkyl; (Ci-C6)alkoxy; nitro; carboxyl; (Ci-C6)alkoxycarboxyl; and T may represent 0x0 in the case where it substitutes a saturated or unsaturated heterocycle; or alternatively T represents (Ci-C6)alkoxycarbonyl(Ci-C6)alkyl; or (Ci-Cβ)alkyl- carbonyl((Ci-C6)alky!)n-, in which n is O or 1. More preferably, when R1 is C6-CiO aryl, R1 represents phenyl. Another preferred group of compounds of the invention consists of compounds for which R2 and R3 together represent a C3-C7 alkylene chain and more preferably R2 and R3 together represent an alkylene chain -(CH2)3- or -(CH2),-. Another even more preferred group of compounds of the invention consists of compounds for which, with R1 being substituted and/or fused aryl, as defined above, R2 and R3 together represent a C3-C7 alkylene chain and more preferably R2 and R3 together represent an alkylene chain -(CH2)3- or -(CH2)4-; and R is a hydrogen atom. Another preferred group of compounds of the invention consists of compounds for which R2 and R3 each represent a hydrogen atom. More particularly, the preferred compounds of the formula (I) are those chosen from: • 2-(4'-methoxybiphenyl-4-yloxy)hex-5-enoic acid; • 2-(4'-fluorobiphenyl-4-yloxy)hex-5-enoic acid; • 2-(4'-phenoxyphenoxy)hex-5-enoic acid; • 4-cyclohex~1-enyl-2-[4-(2-methylthiazol-4-yl)phenoxy]butanoi c acid; • 4-cyclohex-1-enyl-2-[4-(trifluoromethyl)phenoxy]butanoic acid; • 4-cyclohex-1-enyl-2-(4'-methoxy-1 ,1'-biphenyl-4-yloxy)butanoic acid; • 2-[4-(5-chlorothiophen-2-yl)phenoxy]-4-cyclohex-1-enylbutano ic acid; • 2-(4-chlorophenoxy)-4-cyclohex-1-enylbutanoic acid; • 2-(4-benzo[b]thiophen-2-ylphenoxy)-4-cyclohex-1 -enylbutanoic acid; • 2-(4-benzo[b]thiophen-3-ylphenoxy)hex-5-enoic acid; • 2-(3'-fluorobiphenyl-4-yloxy)hex-5-enoic acid; • 2-(4-trifluoromethylphenoxy)hex-5-enoic acid; • 2-[4-(2-methylthiazol-4-yl)phenoxy]hex-5-enoic acid; • 2-(2',5'-dimethylbiphenyl-4-yloxy)hex-5-enoic acid; • 2-(4'-trifluoromethoxybiphenyl-4-yloxy)hex-5-enoic acid; • 2-(4'-chlorobiphenyl-4-yloxy)hex-5-enoic acid; and • 2-[3-(quinolin-2-ylmethoxy)phenoxy]hex-5-enoic acid. The invention also relates to pharmaceutical compositions compris¬ ing a pharmaceutically effective amount of at least one compound of the for¬ mula (I) as defined above in combination with one or more pharmaceutically acceptable vehicles. These compositions can be administered orally in the form of tablets, gel capsules or granules with immediate release or controlled release, intra¬ venously in the form of an injectable solution, transdermal^ in the form of an adhesive transdermal device, or locally in the form of a solution, cream or gel. A solid composition for oral administration is prepared by adding to the active principle a filler and, where appropriate, a binder, a disintegrating agent, a lubricant, a colorant or a flavour enhancer, and by forming the mix¬ ture into a tablet, a coated tablet, a granule, a powder or a capsule. Examples of fillers include lactose, corn starch, sucrose, glucose, sorbitol, crystalline cellulose and silicon dioxide, and examples of binders include polyvinyl alcohol), polyvinyl ether), ethylcellulose, methylcellulose, acacia, gum tragacanth, gelatine, shellac, hydroxypropylcellulose, hydroxy- propylmethylcellulose, calcium citrate, dextrin and pectin. Examples of lubri¬ cants include magnesium stearate, talc, polyethylene glycol, silica and hard- ened plant oils. The colorant can be any of those permitted for used in medicaments. Examples of flavour enhancers include cocoa powder, mint in herb form, aromatic powder, mint in oil form, borneol and cinnamon powder. Obviously, the tablet or granule can be suitably coated with sugar, gelatine or the like. An injectable form comprising the compound of the present invention as active principle is prepared, where appropriate, by mixing the said com¬ pound with a pH regulator, a buffer agent, a suspension agent, a solubilizer, a stabilizer, an isotonic agent and/or a preserving agent, and by converting the mixture into a form for intravenous, subcutaneous or intramuscular injec- tion, according to a standard process. Where appropriate, the injectable form obtained can be freeze-dried via a standard process. Examples of suspension agents include methylcellulose, polysorbate 80, hydroxyethylcellulose, acacia, powdered gum tragacanth, sodium carboxymethyicellulose and polyethoxylated sorbitan monolaurate. Examples of solubilizers include castor oil solidified with polyoxy- ethylene, polysorbate 80, nicotinamide, polyethoxylated sorbitan monolaurate and the ethyl ester of castor oil fatty acid. In addition, the stabilizer encompasses sodium sulfite, sodium meta- sulfite and ether, while the preserving agent encompasses methyl p-hydroxy- benzoate, ethyl p-hydroxybenzoate, sorbic acid, phenol, cresol and chloro- cresol. The present invention also relates to the use of a compound of the formula (I) of the invention for the preparation of a medicament for the pre¬ vention of or treating dyslipidaemia, atherosclerosis and diabetes. The effective administration doses and posologies of the compounds of the invention, intended for the prevention or treatment of a disease, dis¬ order or condition caused by or associated with modulation of PPAR activity, depends on a large number of factors, for example on the nature of the inhi¬ bitor, the size of the patient, the aim of the desired treatment, the nature of the pathology to be treated, the specific pharmaceutical composition used and the observations and the conclusions of the treating physician. For example, in the case of an oral administration, for example a tablet or a gel capsule, a possible suitable dosage of the compounds of the formula (I) is between about 0.1 mg/kg and about 100 mg/kg of body weight per day, preferably between about 0.5 mg/kg and about 50 mg/kg of body weight per day, more preferably between about 1 mg/kg and about 10 mg/kg of body weight per day and more preferably between about 2 mg/kg and about 5 mg/kg of body weight per day of active material. If representative of body weights of 10 kg and 100 kg are considered in order to illustrate the oral daily dosage range that can be used and as described above, suitable dosages of the compounds of the formula (I) will be between about 1-10 mg and 1000-10 000 mg per day, preferably between about 5-50 mg and 500-5000 mg per day, more preferably between about 10.0-100.0 mg and 100.0-1000.0 mg per day and even more preferably between about 20.0-200.0 mg and about 50.0-500.0 mg per day of active material comprising a preferred compound. These dosage ranges represent total amounts of active material per day for a given patient. The number of administrations per day at which a dose is administered can vary within wide proportions depending on pharma¬ cokinetic and pharmacological factors, such as the half-life of the active material, which reflects its rate of catabolism and clearance, and also the minimum and optimum levels of the said active material, in blood plasma or in other bodily fluids, which are reached in the patient and which are required for therapeutic efficacy. Many other factors should also be taken into consideration when determining the number of daily administrations and the amount of active material that should be administered in a single dosage intake. Among these other factors, and not the least of which, is the individual response of the patient to be treated. The present invention also relates to a general process for the prepa¬ ration of the compounds of the formula (I), by reacting a compound of the formula (II) with an alcohol of the formula R1-OH, according to the following reaction scheme:

in which reaction scheme R1, R2, R3 and R are as defined above for formula (I) and X represents -OH or a halogen atom, such as chlorine. When X represents -OH, this reaction is preferably performed in a polar aprotic solvent, such as a linear or cyclic ether, for example diethyl ether, di-tert- butyl ether, diisopropyl ether or dimethoxyethane, or alternatively, such as diox- ane or tetrahydrofuran, tetrahydrofuran and dimethoxyethane being preferred. According to one preferred embodiment of the invention, the molar ratio of the compound of the formula (II) to the alcohol R1 -OH ranges between 0.9 and 1.5, an approximately stoichiometric ratio of between 0.9 and 1.3 and pref¬ erably between 0.9 and 1.1 being desirable. In order to facilitate the reaction, it is desirable to add to the medium a coupling agent, such as a lower alkyl (i.e. C-i-Cβ alkyl) azodicarboxylate, for example ethyl azodicarboxylate. When it is present in the reaction medium, the coupling agent is incor¬ porated into the medium in a proportion of from 1 to 5 equivalents and better still in a proportion of from 1 to 3 equivalents, for example in a proportion of from 1 to 2 molar equivalents relative to the initial amount of compound of the formula (II). Preferably, it is also recommended to introduce a phosphine into the reaction medium, such as triphenylphosphine. In this case, the molar ratio of triphenylphosphine to the compound of the formula (II) is preferably maintained between 1 and 5, for example between 1 and 3 and especially between 1 and 2. When X represents a halogen atom, the solvent is preferably of ketonic type and a base, preferably a mineral base chosen from sodium hydroxide, potassium hydroxide, sodium hydrogen carbonate, potassium hydrogen carbonate, sodium carbonate and potassium carbonate, is intro¬ duced into the reaction medium. Usually, the molar ratio of the base to the compound of the formula (II) ranges between 1 to 5 and better still between 1 to 3. When X represents a halogen atom, the reaction temperature gener¬ ally ranges between 100C and 1200C, for example between 6O0C and 100°C and better still between 7O0C and 9O0C. When X represents -OH, the reaction temperature generally ranges between -15°C and 5O0C, it being understood that temperatures of between -150C and 1O0C are desirable in the presence of a coupling agent. The compounds of the formula (I) in which R represents H can advantageously be obtained by saponification of the corresponding com¬ pounds of the formula (I) in which R represents a Ci-C10 alkyl radical. The saponification can be performed via the action of a base, such as a mineral base chosen from lithium hydroxide, potassium hydroxide, sodium hydroxide, sodium hydrogen carbonate, potassium hydrogen carbonate, sodium car¬ bonate and potassium carbonate. The molar amount of base to be used gen¬ erally ranges from 1 to 20 equivalents and preferably from 1 to 12 equiva¬ lents depending on the strength of the selected base. More particularly, in the case of lithium hydroxide (LiOH), it is pre¬ ferred to react together from 8 to 12 equivalents of base relative to the amount of ester of the formula (I) present in the reaction medium. The reaction is preferably performed in a solvent of polar protic type and more preferably in a mixture of lower (CrC4) alkanol and water, such as a mixture of ethanol and water or of methanol and water. The reaction temperature advantageously ranges between 35°C and 1200C and better still between 400C and 1000C. Methods A to D below are variants of the general process described above.

METHOD A When X represents OH, a preferred embodiment of the general preparation process according to the invention follows the reaction scheme below:

(Aa) : THF / PPh3 / DEAD / room temp. (Ab) : EtOH / KOH / H2O reflux

in which reaction scheme R1, R2 and R3 are as defined above for formula (I), R1 represents R as defined above, with the exception of hydro¬ gen, the compound (IIOH) being the compound of the formula (II) in which X represents -OH; the compound (IR-) being the compound of the formula (I) in which R1 represents an alkyl radical and the compound (IOH) being the com¬ pound of the formula (I) in which R represents hydrogen. THF means tetra- hydrofuran, PPh3 means triphenylphosphine, DEAD means diethyl azodicar- boxylate, "room temp." means room temperature, EtOH is ethanol and KOH is potassium hydroxide. In the above reaction scheme, the saponification reaction step (Ab) is optional, i.e. it is performed only in the case where the desired compound of the formula (I) is a carboxylic acid (R = H). This embodiment and the compounds of the formula (I) thereby obtained are illustrated in Examples 1 and 2.

METHOD B According to one embodiment of the process according to the inven- tion, the compounds of the formula (IG), which is a special case of the com¬ pounds of the formula (I) in which R1 represents an aryl radical substituted by a radical G, as defined above, can advantageously be prepared according to the following reaction scheme:

(Ba) : CH3OCH2CH2OCH3 / Pd(PPh3)4 / Na2CO3 / H2O (Bb) : EtOH / KOH / H2O / reflux

in which reaction scheme: - R2 and R3 are as defined above for formula (I) ; - R1 represents R1 as defined above, with the exception of hydrogen; - R11 represents R1, as defined above, bearing a group that is reactive with the derivative of the formula (IV) and chosen especially from a bromine or iodine atom and a CF3SO3- radical, bromine and iodine being the preferred reactive groups; and - R12 represents R11Jn which the group that is reactive with the derivative of the formula (IV) has been substituted by the radical G. As indicated in the above reaction schemes, the saponification step (Bb) is optional. The compounds of the formulae (IG, RO and (IG, H) form the set of compounds of the formula (IG), which is a special case of the compounds of the formula (I) in which R1 represents an aryl radical substituted by a radi¬ cal G. Thus, the compounds of the formula (I) in which R1 represents aryl sub¬ stituted by a monocyclic, bicyclic or tricyclic aromatic heterocyclic group com¬ prising one or more hetero atoms chosen from O, N and S, and optionally sub- stituted by one or more radicals T as defined above, or alternatively in which R1 represents an aryl group optionally substituted by one or more radicals T, can be prepared by reaction of the corresponding compound of the formula (I) in which R1 represents aryl substituted by a halogen atom, such as chlorine, bro¬ mine or iodine, with a compound of the formula (IV) defined in the above reac- tion scheme, in which G represents a monocyclic, bicyclic or tricyclic aromatic heterocyclic group comprising one or more hetero atoms chosen from O, N and S, and optionally substituted by one or more radicals T as defined above when R1, in the final compound, represents aryl substituted by such a hetero- cyclic group, or alternatively G represents arylOptionally substituted by one or more radicals T when, in the final compound, R1 represents aryl substi¬ tuted by an aryl group, which is itself optionally substituted by one or more radicals T. Advantageously, from 1.5 to 5 equivalents and preferably from 1.5 to 3 equivalents of the compound of the formula (IV) are incorporated relative to the amount of compound of the formula (III) present in the reaction medium. This reaction is preferably performed in a polar aprotic solvent in the presence of a palladium 0 complex and a base. A linear or cyclic ether, such as those defined above is more par- ticularly suitable as solvent. Dimethoxyethane is preferred. The base that will be used is any of the mineral bases mentioned above and advantageously sodium carbonate. For example, from 1.5 to 5 equivalents and preferably from 1.5 to 3 equivalents of base, relative to the amount of compound of the formula (III), can be introduced into the reaction medium. According to one preferred embodiment, the amounts of base and of compound of the formula (IV) are equivalent. The amount of palladium 0 complex used is catalytic. Usually, from 0.001 to 1 equivalent and preferably from 0.01 to 0.1 equivalent of the said complex is used. An example of a palladium 0 complex that can be used is tetrakis(triphenylphosphine)- palladium 0. The reaction temperature advantageously ranges between 5O0C and 12O0C and preferably between 70°C and 90°C. This embodiment and the compounds resulting therefrom are illus- trated in Examples 3 and 4. METHOP C In the starting compound of the formula (II) defined above, when X represents halogen, for example a chlorine atom, one preferred embodiment of the process according to the invention adopts the following reaction scheme:

in which reaction scheme R1, R2 and R3 are as defined above for formula (I), R1 represents R, as defined above, with the exception of hydro- gen, the compound (Net) being the compound of the formula (II) in which X represents a chlorine atom, the compound (IR>) being the compound of the formula (I) in which R represents an alkyl radical, and the compound (IOH) being the compound of the formula (I) in which R represents hydrogen. The set of compounds of the formulae (IR>) and (IOH) together form the set of com- pounds of the formula (I) according to the invention. MIBK means methyl iso- butyl ketone, K2CO3 means potassium carbonate, MeOH is methanol and LiOH is lithium hydroxide. In the above reaction scheme, the saponification reaction step (Cb) is optional, i.e. it is performed only in the case where the desired compound of the formula (I) is a carboxylic acid (R = H). This embodiment, and the compounds of the formula (I) thereby obtained, are illustrated in Examples 5 and 6. METHOD D The compounds of the formula (I) can also be prepared according to a synthetic route using compounds grafted onto a resin of Wang bromo type, according to the following reaction scheme:

CH2CI2, r.t., 18 h in which scheme R1, R2 and R3 are as defined for the general formula CO- ln the above reaction scheme, a mixture of α-hydroxy acid and cae¬ sium carbonate, in a polar aprotic solvent, for instance dimethylformamide, is treated with a suspension of resin, so as to obtain the resin-grafted α- hydroxy acid derivative. The alcohol R1-OH is then added to this derivative in the presence of a phosphine, such as 4,4-dimethyl-2-(triphenyIphosphanyl)(1 ,2,5)-thiadiazoli- dine. The reaction is performed, generally at room temperature, for a time possibly ranging from one to several hours, for example about 18 hours. The compound is then detached from the resin according to standard techniques, for example using trifluoroacetic acid, to give the carboxylic acid of the formula (IOH) obtained in the last step of the above reaction scheme. This carboxylic acid is a special case of the compound of the formula (I) in which R represents hydrogen, and can optionally be readily converted into a compound of the formula (I) in which R has the definition indicated above for the set of compounds according to the invention, with the exception of hydro¬ gen, via any method known per se. This embodiment, and the compounds of the formula (I) thereby obtained, are illustrated in Example 7. In the processes described above, it should be understood that the operating conditions can vary substantially depending on the various sub- stituents present in the compounds of the formula (I) that it is desired to pre¬ pare. Such variations and adaptations are readily available to a person skilled in the art, for example from scientific reviews, the patent literature, Chemical Abstracts, and computer databases, including the Internet. Simi¬ larly, the starting materials are either commercially available or are available via syntheses that a person skilled in the art can readily find, for example in the various publications and databases described above. The optical isomers of the compounds of the formula (I) can be obtained, on the one hand, via standard techniques for separating and/or purifying isomers, known to those skilled in the art, from the racemic mixture of the compound of the formula (I). The optical isomers can also be obtained directly via stereoselective synthesis of an optically active starting compound. The examples that follow illustrate the present invention without lim¬ iting it in any way. In these examples and in the proton nuclear magnetic resonance (300 MHz NMR) data, the following abbreviations have been used: s for singlet, d for doublet, t for triplet, q for quartet, o for octet and m for complex multiplet. The chemical shifts δ are expressed in ppm. "M. p." means "melting point".

EXAMPLES

Example 1 : Process for the preparation of ethyl 2-[(4-trifluoromethyl- phenyI)oxy]-4-cyclohex-1 -en-1 -ylbutanoate. 1.1 g (0.0071 mol) of 4-trifluoromethylphenol and 1.5 g (0.0071 mol) of ethyl 4-cyclohex-1-en-1-yl-2-hydroxybutanoate (B. B. Snider, J. Org. Chem., (1984), 1688-1691) are added to a solution of 2.8 g (0.0071 mol + 50%) of triphenylphosphine in 70 ml of tetrahydrofuran (THF), and a solution of 1.8 g (0.0071 mol + 50%) of diethyl azodicarboxylate (DEAD) in 7 ml of THF are added, at O0C. The solution is allowed to return to room temperature with stirring, and is reacted overnight. The reaction medium is concentrated, taken up in 1 N sodium hydroxide (NaOH) solution and extracted with ethyl acetate (EtOAc). The extract is washed with saturated sodium chloride (NaCI) solution and then dried over sodium sulfate (Na2SO4). After concen¬ trating, the oil obtained is taken up in 150 ml of an ether/hexane mixture: a white precipitate (O=PPh3) is formed, which is removed by suction-filtering. The solution is concentrated again. The product is purified by flash chromatography (98/2 heptane/ethyl acetate). 2.0 g of a colourless oil are obtained. Yield = 80% 1H NMR (CDCI3, 300 MHz): 1.45 (3H, t, J =7 Hz); 1.71-1.87 (4H, m); 2.15-2.35 (8H, m); 4.39-4.46 (2H, q, J = 7 Hz); 4.84 (1 H, t, J = 6 Hz); 5.61 (1 H, s); 7.14 (2H, d, J = 8 Hz); 7.74 (2H, d, J = 8 Hz).

Example 2: Process for the preparation of 4-cyclohex-1-enyl-2-[4- (trifluoromethyl)phenoxy]butanoic acid The ester obtained above (1.8 g; 0.005 mol) is dissolved in 20 ml of ethanol. After addition of 1.7 g of 85% potassium hydroxide (KOH) (5 equivalents), the solution is refluxed for 30 minutes. After adding 10 ml of water, refluxing is continued for 4 hours. The reaction medium is concen¬ trated. The oil obtained is taken up in water and washed with ether. The aqueous phase is acidified with 1 N hydrochloric acid (HCI) and then extracted with ethyl acetate. The extract is dried over Na2SO4 and then con¬ centrated. The solid obtained is recrystallized from 50 ml of heptane. 1.1 g of a white solid are obtained. Yield = 75% m.p.: 109-1110C 1H NMR (CDCI3, 300 MHz): 1.36-1.76 (4H, m); 1.76-2.02 (4H, m); 4.02-2.29 (4H1 m); 4.68 (1 H, m); 5.39 (1 H, s); 6.94 (2H, d, J = 8.3 Hz); 7.54 (2H, d, J = 8.3 Hz). Mass spectrometry: (ES) M-H = 327.2

Example 3: Process for the preparation of ethyl 2-[4-(5-chlorothiophen- 2-yi)-phenoxy]-4-cyclohex-1-enylbutanoate 0.18 g (0.04 equivalent) of Pd(PPh3)4 and then 1.2 g (0.0084 mol) of δ-chloro-2-thiopheneboronic acid are added to a solution of 1.4 g (0.0038 mol) of ethyl 2-[(4-bromophenyl)oxy]-4-cyclohex-1-en-1-ylbutanoate in 20 ml of dimethoxyethane. 4.2 ml of 2M sodium carbonate solution are added at room temperature. The reaction mixture is stirred overnight and then refluxed for 2 hours. After cooling to room temperature, the mixture is taken up in water and extracted with ethyl acetate. The extract is washed with 1N sodium hydroxide and then with saturated aqueous NaCI solution and finally dried over Na2SO4. After concentrating, the black oil obtained is purified by flash chromatography (95/5 heptane/ethyl acetate). 1.1 g of a thick oil are obtained. Yield = 73% 1H NMR (CDCI3, 300 MHz): 1.48 (3H1 1, J = 7 Hz); 1.78-1.88 (4H, m); 2.18-2.38 (8H, m); 4.42-4.49 (2H, q, J = 7 Hz); 4.83 (1H, t, J = 6Hz); 5.56 (1H, s); 7.07-7.18 (4H, m); 7.61 (2H1 d, J = 8 Hz).

Example 4: Process for the preparation of 2-[4-(5-chlorothiophen-2-yl)- phenoxy]-4-cyclohex-1-enylbutanoic acid The ester obtained above in Example 3 (1.1 g, 0.0027 mol) is dis¬ solved in 25 ml of ethanol. 0.5 g (0.0081 mol) of 85% potassium hydroxide is added and the mixture is refluxed for 30 minutes. 12.5 ml of water are added and refluxing is continued for a further 4 hours. After cooling to room tem- perature, the reaction medium is concentrated, taken up in water and washed with ether. The aqueous phase is acidified with 1N HCI. The white precipitate formed is extracted with dichloromethane and dried over Na2SO4. 0.9 g of a cream-coloured solid melting at 136-138°C is obtained. Yield = 90% 1H NMR (CDCI3, 300 MHz): 1.40-1.73 (4H1 m); 1.81-2.03 (4H, m); 2.03-2.28 (4H, m); 4.66 (1 H, m); 5.41 (1 H, s); 6.76-7.02 (4H, m); 7.34-7.51 (2H1 m).

Example 5: Process for the preparation of methyl 4-cyclohex-1-en-1-yl- 2-[(4'-methoxy-1,1'-biphenyl-4-yl)oxy]butanoate 1.9 g (0.0138 mol) of potassium carbonate are added to a solution of 1.4 g (0.0069 mol) of 4'-methoxy-1 ,1'-biphenyl-4-ol in 30 ml of 3-methyl-2- pentanone (MIBK). The mixture is refluxed for 30 minutes and a solution of 1.5 g (0.0069 mol) of methyl 2-chloro-4~cyclohex-1-en-1-ylbutanoate in 10 ml of 3-methyl-2-pentanone is then added. Refluxing is continued for a further 6 hours. After cooling to room temperature, the reaction medium is concentrated, taken up in water and extracted with ethyl acetate. The extracts are washed with 1 N sodium hydroxide and then with saturated aqueous NaCI solution, and dried over Na2SO4. After concentrating, a thick oil is obtained, which is purified by flash chromatography (95/5 heptane/ethyl acetate). 1.1 g of an oily product are thus obtained. Yield = 42% 1H NMR (CDCI3, 300 MHz): 1.43-1.47 (4H, m); 1.88-2.10, 8H, m); 3.66 (3H, s); 3.75 (3H, s); 4.57 (1 H, t, J = 6 Hz); 5.36 (1 H, s); 6.83-6.89 (4H, m); 7.36-7.41 (4H, m).

Example 6: Process for the preparation of 4-cyclohex-1-enyl-2-(4'- methoxy-1 ,1 '-biphenyl-4-y loxy)butanoic acid The ester obtained above in Example 5 (1.0 g, 0.0026 mol) is dis¬ solved in 20 ml of methanol. A solution of 26 ml of 1 M LiOH-H2O is added at room temperature. The milky suspension is refluxed for 1 hour. After con¬ centrating the reaction medium, the white solid obtained is taken up in 14 HCI. The suspension is stirred for 30 minutes and then extracted with ethyl ace- tate. After concentrating, 0.6 g of a white solid with a melting point of 152- 1540C is obtained. Yield = 63% 1H NMR (CDCI3, 300 MHz): 1.42-1.74 (4H, m); 1.82-2.04 (4H, m); 2.04-2.36 (4H, m); 3.83 (3H1 s); 4.68 (1H, m); 5.42 (1H, s); 6.95 (4H, m); 7.46 (4H, m).

Example 7: Process for the preparation of 4-cyclohex-1-enyl-2-[4-(2- methoxycarbonylvinyl)phenoxy]butanoic acid A 20% solution of caesium carbonate in water (23 ml, 14.4 mmol) is added to a solution of 4-cyclohex-1-enyl-2-hydroxybutyric acid (7 g, 38 mmol) in methanol (200 ml). After stirring for 10 minutes, the solvents are evapo¬ rated off and the residue is taken up in toluene, which is then evaporated off. The residue is taken up in dimethylformamide (DMF) (125 ml), and a sus- pension of Wang bromo resin (23.7 g, 18 mmol) in DMF (125 ml) is then added. The mixture is stirred for 18 hours at 600C. The resin is then washed several times with THF (3 x 150 ml, 2 minutes), 1/1 THF/H2O (3 * 150 ml, 2 minutes), methanol (MeOH) (3 * 150 ml, 2 minutes), dichloromethane (3 * 150 ml, 2 minutes) and MeOH (3 x 150 ml, 2 minutes). The resin is dried under vacuum at 5O0C. A solution of ethyl 3-(4-hydroxyphenyl)prop-2-enoate (1 mmol) in di¬ chloromethane (2 ml) is added to the grafted resin (150 mg, 0.1 mmol). A solution of 4,4-dimethyl-2-(triphenylphosphanyl)-1 ,2,5-thiadiazolidine (1 mmol) in dichloromethane (8 ml) is then added and this suspension is stirred at room temperature for 18 hours. The resin is filtered and washed with DMF (5 ml), 50/50 DMF/H2O (5 ml), MeOH (2 x 5 ml) and 80/20 DCM/DCE (3 x 5 ml). The resin is then treated with a 20/80 solution of TFA/DCM (trifluoroacetic acid/dichloromethane) for 15 minutes. The resin is filtered off and washed with dichloromethane (2 x 5 ml). The filtrate is evaporated and the residue is purified by preparative LCMS to give 3.20 mg of the expected product in the form of an oil. Mass spectrometry = M-H: 343.3 According to protocols similar to those described for obtaining the compounds of Examples 1 to 7 above, the compounds presented in Table 1 below were obtained.

RESULTS

The activity of the compounds of the invention leading to a hypolipid- aemiant and hypoglycaemiant effect was demonstrated in vitro and in vivo by performing the following tests: The measurement of the PPAR activation was performed according to a technique described by Lehmann et a/. (J. Biol. Chem., 270, (1995), 12953-12956). CV-1 cells (monkey kidney cells) are co-transfected with an expres¬ sion vector for the chimeric proteins PPARa-GaW or PPARγ-Gal4 and with a "reporter" plasmid that allows the expression of the luciferase gene placed under the control of a promoter comprising GaW response elements. The cells are plated into 96-well microplates and co-transfected using a commercial reagent with the reporter plasmid (pG5-tk-pGL3) and the expression vector for the chimeric protein (PPARa-GaW or PPARγ-Gal4). After incubating for 4 hours, whole culture medium (comprising 10% foetal calf serum) is added to the wells. After 24 hours, the medium is removed and replaced with whole medium comprising the test products (50 μM, 25 μM and 12.5 μM final). The products are left in contact with the cells for 18 hours. The cells are then lysed and the luciferase activity is measured using a lumi- nometer. A PPAR activation factor can then be calculated by means of acti¬ vation of the expression of the reporter gene induced by the product (relative to the control cells that have not received any product). By way of example, the compound of Example 2 at a concentration of 50 μM, activates the chimeric protein PPARα-Gal-4 by a factor of 24.9, and the chimeric protein PPARγ-Gal4 by a factor of 9.3, relative to the activity of the receptor without ligand. In the absence of the binding domain for the PPAR a or γ ligand (vector expressing Gal4 alone), the luciferase activity measured in the presence of this product is zero. The following results were obtained with concentrations of 50 μM, 25 μM and 12.5 μM on the chimers α and y.

The antidiabetic and hypolipidaemiant activity of the compounds was determined orally on db/db mice. 17-week-old db/db mice are treated orally for 15 days with the com¬ pound of Example 2 (100 mg/kg/day). Each group studied comprises seven animals. After treatment for 15 days, retro-orbital samples are taken under mild anaesthesia and after fasting for four hours. The following parameters were measured: Assay of the glycaemia (glucose oxidase) and of the lipid parameters on the sera at D15 (COBAS): triglycerides, total cholesterol (CHOL), HDL cholesterol (HDL-C) and free fatty acids (FFA) (BioMerieux and Waco Chemicals assay kit). The results obtained are given in the table below. The measurements reported represent mean values ± standard error. % var.: percentage of variation versus control. Mann-Whitney test: *: p < 0.05 versus control **: p < 0.01 versus control ns: not significant These results demonstrate the antidiabetic and hypolipidaemiant activity of the compounds of the invention on triglycerides and free fatty acids. The marked increase in the level of HDL cholesterol with these same compounds should be noted.