The present invention is directed to polyphenolic polymers formed from dihydroxybenzoicacid (DHB) derivatives or from resorcinol derivatives, monomers which formsuch polymers, blends of the polymers with drugs and/or additional polymers,as well as medical devices formed from, coated with, impregnated by or coveringsmade with any of the foregoing polymers (with or without drugs) or blends (withor without drugs).