In this paper, we extend the concept of stability to vertical collusive agreements, involving downstream and upstream firms, using a setup of successive Cournot oligopolies. We show that a stable vertical agreement always exists: the unanimous vertical agreement involving all downstream and upstream firms. Thus, stable vertical collusive agreements exist even for market structures in which horizontal cartels would be unstable. We also show that there are economies for which the unanimous agreement is not the only stable one. Furthermore, Stigler statement according to which the only ones who benefit from a collusive agreement are the outsiders need not be valid in vertical agreements.