Abstract: A phosphine derivative of the following general formula ( I ): ##STR1## (wherein R.sup.1 is an alkyl group having 1 to 18 carbon atoms or an aryl group having 6 to 18 carbon atoms, and the aryl group may have an alkyl group having 1 to 18 carbon atoms or an alkenyl group having 2 to 18 carbon atoms) is reacted with acrylic acid or methacrylic acid in the presence of a catalyst selected from the group consisting of an organic peroxide and an azo-compound, and the resulting reaction product is hydrolyzed with water, thereby to obtain a phosphinyl-carboxylic acid derivative of the following general formula (III): ##STR2## (wherein R.sup.1 is as defined above, and R.sup.2 is a hydrogen atom or a methyl group). Based on the reaction above-mentioned, ester of free acid and a cyclic acid anhydride can also be obtained. Accordingly, the target compound can be obtained at a relatively low reaction temperature in a short period of time with high yield.