We propose a new criterion for equilibria of extensive games, in the spirit of Selten's
perfectness criteria. This criterion requires that players' strategies be sequentially
rational: Every decision must be part of an optimal strategy for the remainder of
the game. This entails specification of players' beliefs concerning how the game
has evolved for each information set, including information sets off the equilibrium
path. The properties of sequential equilibria are developed; in particular, we study
the topological structure of the set of sequential equilibria. The connections with
Selten's trembling-hand perfect equilibria are given.