PURPOSE: To obtain the subject polymer having a number-average mol.wt. and an iodine value in specific ranges, respectively, and having a higher melting point than a specific value, solid at room temperature, having an extremely high addition rate, easy in production, and useful as a raw material for aqueous coatings.

CONSTITUTION: This polymer has a number-average mol.wt. of 1000-100000, an iodine value of 10-390, and a melting point of ≥50°C. The polymer is produced by reacting (A) a conjugated dienic polymer having a number-average mol.wt. of 500-100000 with (B) maleic anhydride preferably in a component A/B weight ratio of 10/90 to 90/10 in the presence of oxygen and/or an organic peroxide (e.g. benzoyl peroxide) as a catalyst in an organic solvent. The reaction is preferably performed at 50-150°C for 10min to 10hrs under stirring. The concentration of the total resins of the components A and B on the reaction is preferably 5-50wt.%.