The invention provides medical devices comprising high-strength alloys which degrade over time in the body of a human or animal, at controlled degradation rates, without generating emboli. In one embodiment the alloy is formed into a bone fixation device such as an anchor, screw, plate, support or rod. In another embodiment the alloy is formed into a tissue fastening device such as staple. In yet another embodiment, the alloy is formed into a dental implant or a stent.