Biodegradable poly(ester-amides) are synthesized from amino acids, diols and dicarboxylic acids where one or both of the diols and dicarboxylic acids contain unsaturation; e.g., from di-p-nitrophenyl dicarboxylates and p-toluenesulfonic acid salts of bis(alpha-amino acid) disesters of diols where one or both of the dicarboxylate and diol moieties contain unsaturation or from di-p-nitrophenyl dicarboxylates, and p-toluene-sulfonic acid salts of bis(alpha-amino acid) diesters of diols and p-toluenesulfonic acid salt of lysine ester where one or both of the dicarboxylate and diol moieties contain unsaturation. The polymers are useful as biodegradable carriers for drugs of other bioactive agents.