Group Diffie-Hellman protocols are a natural extension of the well-known two-party Diffie-Hellman key exchange protocol. While the security of the two-party DH key exchange is directly based on the intractability of two-party Decisional Diffie-Hellman problem, there is no natural extension of this problem to an n-party protocol. In this paper, we present a simple model for the analysis of security of this family of protocols. We apply our approach in analyzing Cliques protocol, as an example of this family of protocols, where we have found some weaknesses. These weaknesses enable a dishonest former member to compromise the secret session key, even if he is no longer belongs to the group. We suggest modifications to these protocols that can avoid the discovered weaknesses.