A device implantable into a human or animal body comprising a biodegradable polymer which comprises ethylene carbonate units of the formula A <;?in-line-formulae description="In-line Formulae" end="lead"?>;-(-C(O)-O-CH<;SUB>;2<;/SUB>;-CH<;SUB>;2<;/SUB>;-O-)- A <;?in-line-formulae description="In-line Formulae" end="tail"?>; having an ethylene carbonate content of 70 to 100 Mol %, an intrinsic viscosity of 0.4 to 4.0 dl/g measured in chloroform at 20° C. at a concentration of 1 g/dl and a glass transition temperature of from 5 to 50° C., degradable by surface erosion which is governed by a non-hydrolytic mechanism.