Process for the preparation of polycarbonates by reacting at least one epoxy compound with carbon dioxide at 40.degree. to 200.degree. C. and 2 to 40 bar in the presence of a catalytic amount of a double metal cyanide complex and (a) one or more salts composed of at least bivalent metal ions and metal-free anions having a solubility in water of at least 1 g/100 ml at 25.degree. C., and/or (b) one or more no-metal containing acids of which a 0.1 N solution in water at 25.degree. C. has a pH not exceeding 3.