The invention provides elastomeric copolyester amides, elastomeric copolyester urethanes, and methods for making the same. The polymers are based on .alpha.-amino acids and possess physical, chemical and biodegradation properties that render them suitable for use in the human body. The polymers are useful as carriers of drugs or other bioactive substances. The polymers can also be linked, intermixed, or a combination thereof, to one or more drugs. Additionally, the polymers can be used to coat stents, for example, to suppress restenosis. Furthermore, the biodegradation of the copolyester amides and copolyester urethanes allows for the delivery of essential .alpha.-amino acids to sites in the body, for example, to facilitate wound repair of injured tissues.