The present invention provides biodegradable polymer particle delivery compositions based on polymers, such as polyester amide (PEA) and polyester urethane (PEUR) polymers, that contain amino acids in the polymer. The polymer particle delivery compositions can be formulated as a liquid dispersion of polymer particles with the bioactive agents dispersed in the particle or conjugated attached to polymer molecules or particle surfaces. The bioactive agents can include drugs, polypeptides, DNA and cells for cell-based therapies using particles sized for local, mucosal or circulatory delivery. Methods of treating a disease by administering to a subject the polymer particle delivery composition, which incorporates a bioactive agent suitable for treatment of the disease, or its symptoms, are also included.