In this paper we consider multilateral stochastic bargaining models withgeneral agreement rules. For n-player games where in each period a player is randomly selected to allocate a stochastic level of surplus and q ≤ n players have to agree on a proposal to induce its acceptance, we characterize the set of stationary subgame  perfect equilibrium payoffs and establish their existence. We show that for agreement rules other than the unanimity rule, the equilibrium payoffs need not be unique. Furthermore, even when the equilibrium is unique, it need not be efficient.