In a proxy signature scheme, a potential signer delegates his capabilities to a proxy signer, who can sign documents on behalf of him. The recipient of the signature verifies both identities: that of the delegator and that of the proxy signer. There are many proposals of proxy signature schemes, but security of them has not been considered in a formal way until the appearance of [2, 8]. If the entities which take part in a proxy signature scheme are formed by sets of participants, then we refer to it as a fully distributed proxy signature scheme [4]. In this work, we extend the security definitions introduced in [2] to the scenario of fully distributed proxy signature schemes, and we propose a specific scheme which is secure in this new model.