A method for synthesizing polyanhydrides in solution using coupling agents and a removable acid acceptor to effect a one-step polymerization of dicarboxylic acids. As used in the method, these coupling agents include phosgene, diphosgene, and acid chlorides. Insoluble acid acceptors include insoluble polyamines and crosslinked polyamines such as polyethyleneimine and polyvinylpyridine and inorganic bases such as K.sub.2 CO.sub.3, Na.sub.2 CO.sub.3, NaHCO.sub.3, and CaCO.sub.3. The only byproduct formed is a removable hydrochloric acid-acid acceptor.Examples are provided of the polymerization of highly pure polyanhydrides using phosgene, diphosgene or an acid chloride as the coupling agent, in combination with either an insoluble acid acceptor or a soluble acid acceptor in a solvent wherein the polymerization byproduct or polymer is insoluble.A particularly important application of these polyanhydrides is in the formation of drug delivery devices containing bioactive compounds. The method is also useful in the polymerization of dicarboxylic acids including heat liable dipeptides of glutamic or aspartic acid.