We propose a much-needed formal definition of security for cryptographic key management APIs. The advantages of our definition are that it is general, intuitive, and applicable to security proofs in both symbolic and computational models of cryptography. Our definition relies on an idealized API which allows only the most essential functions for generating, exporting and importing keys, and takes into account dynamic corruption of keys. Based on this we can define the security of more expressive APIs which support richer functionality. We illustrate our approach by showing the security of APIs both in symbolic and computational models.