This paper formulates the concept of a security equilibrium as a very weak notion of equilibrium for a variety of models of trading of goods under pairwise bargaining of buyers and sellers brought together by some matching process. (Such models have been developed by Rubinstein-Wolinsky and others.) The basic idea in the concept is that it is common knowledge that no player will settle for a payoff (under any contingency) which is less than his security level, given the contingency. The basic result of the paper is the uniqueness of a security equilibrium which, given the weakness of the notion, is a strong result for such models. The notion is then applied for a number of models of pairwise bargaining, generalizing the earlier work. In addition to uniqueness results the paper provides a formula for the equilibrium deal for a steady state version of the model. The final section of the paper extends the previous results for cases in which the beliefs of the players are conditional on history and thus evolve during the process. The resulting notion of a security equilibrium is weaker than the concept of a sequential equilibrium of Kreps and Wilson.