We present a new attack, called the inter-protocol interleaving attack, on authentication and key distribution protocols. The attack enlightens us two things. The first is that when considering attacks against a protocol, we should consider not only the protocol itself, but also the interaction with other protocols. The second is about a warning of `not using the shared secret keys between a server and its clients in any other places' that appears in many security-related communication standards, such as CCITT X.509 and ISO 9798. Our attack provides a concrete example for showing that this warning is necessary.