Multi-proxy signature schemes allow an original signer to authorize a group of proxy members, and only the cooperation of all the signers in the proxy group can generate the proxy signatures on behalf of the original signer. Multi-proxy signature schemes have been suggested to use in a number of applications, particularly in distributed computing where delegation of rights is quite common. Although some work has been done in multi-proxy signature schemes, until now there is no formalized definition and security model for them. In this paper, we will give the formal definition of multi-proxy signature schemes and formalize a notion of security for them. We also propose a specific scheme which is provably secure in the new model.