Thermally stable polymers comprising resorcinol arylate chain members are prepared using an interfacial method comprising the steps of: interfacial method for preparing polymers comprising resorcinol arylate polyester chain members substantially free of anhydride linkages linking at least two mers of the polymer chain, comprising the steps of: (a) preparing an aqueous solution comprising at least one resorcinol moiety, said solution having a pH less than or equal to about 5; (b) after step (a), preparing a mixture comprising the resorcinol moiety, at least one catalyst and at least one organic solvent substantially immiscible with water; and (c) adding to the mixture from (b) at least one dicarboxylic acid dichloride while maintaining the pH between 3 and 8.5 through the presence of an acid acceptor, wherein the total molar amount of acid chloride groups is stoichiometrically deficient relative to the total molar amount of phenolic groups.