A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. We consider distributed gossip protocols wherein the agents themselves instead of a global scheduler determine whom to call. In this paper the problem of designing and analyzing gossip protocols is given a dynamic twist by assuming that when a call is established not only secrets are exchanged but also telephone numbers. Both numbers and secrets can be represented by edges in a gossip graph. Thus, each call may change both the number relation and the secret relation of the graph. We define various such distributed dynamic gossip protocols, and we characterize them in terms of the class of graphs where they terminate successfully.