Poly(beta-malic acid) derivatives bearing a lateral allyl or 3-methyl-3-butenyl ester group have been prepared by anionic ring opening polymerization or copolymerization of 4-allyloxycarbonyl-2-oxetanone or 4-[3-methyl-3-butenyloxycarbonyl]-2-oxetanone and 4-benzyloxycarbonyl-2-oxetanone as comonomer. These new chiral beta-substituted-beta-lactones with unsaturated lateral groups have been synthesized from aspartic acid as precursor and by using allylic alcohol or 3-methyl-3-buten-1-ol for opening bromosuccinic acid anhydride, an intermediate compound in the monomer synthesis route. The proportion of unsaturated lateral groups in the polymer was strictly controlled by the proportion of the corresponding lactone in the initial monomers mixture and can vary up to 100%. Functionalized polyesters have been prepared and characterized, and to test the reactivity of the present double bonds, epoxidation has been carried out by using m-chloroperbenzoic acid and dimethyldioxirane as chemical reagents. The activation of the double bond was depending on its chemical environment and on the polymer composition, but quantitative epoxidation has been achieved.