tradenames of showa shell petroleum chemicals co for vinyl esters of synthetic monocarboxylic acids having 9 and 10 carbon atoms respectively both veova 9 and veova 10 have a branched structure represented by the following formula str1 wherein r 1 r 2 and r 3 are alkyl groups at least one of which is methyl group it is possible to jointly use two or more kinds of carboxylic acid vinyl esters the third component which provides a functional group to the copolymer is a hydroxyl containing allyl ether examples of useful allyl ethers are ethylene glycol monoallyl ether diethylene glycol monoallyl ether triethylene glycol monoallyl ether and a modified allyl ether which is obtained by modifying ethylene glycol monoallyl ether with u03b5 caprolactone and represented by the following formula str2 the amounts of these essential components of the copolymer are limited within the ranges specified hereinbefore respectively in view of the following tendencies if the amount of ctfe is too large the copolymer becomes low in solubilities in organic solvents and besides it becomes difficult to prepare the copolymer at good yield if the amount of ctfe is too small the copolymer becomes insufficient in chemical resistance and weather resistance it is preferred that in the copolymer ctfe amounts to 40 60 mol if the amount of the carboxylic acid vinyl ester is too small the copolymer will become too low in molecular weight and some difficulties will arise in preparing the copolymer if the amount of this component is too large the copolymer becomes insufficient in chemical resistance and weather resistance it is preferred that repeating.