PURPOSE: To improve yield of the aimed compound, by using a specific catalyst containing phosphorus, vanadium, nickel and oxygen in producing acrylic acids or methacrylic acids from acetic acids or propionic acids and formaldehydes.

CONSTITUTION: A raw material gas containing acetic acid and/or an ester thereof or propionic acid and/or an ester thereof and formaldehyde and/or a derivative thereof is brought into contact with a catalyst to produce acrylic acid and/or an ester or methacrylic acid and/or an ester thereof. In the process, a catalyst containing a component expressed by the formula PaVbNicOd (aWd each represent the numbers of P, V, Ni and O atoms; a is 0.8W21; c is 0.2W20; d is the number of atoms required to satisfy the valences of the components except O when b is 1) is used to provide the aimed compound in a higher yield than that in using a conventionally well-known catalyst.