A basic problem in the theory of noncooperative games is the following: which Nash equilibria are strategically stable, i.e. self-enforcing, and does every game have a strategically stable equilibrium? We list three conditions which seem necessary for strategic stability--backwards induction, iterated dominance, and invariance--and define a set-valued equilibrium concept that satisfies all three of them. We prove that every game has at least one such equilibrium set. Also, we show that the departure from the usual notion of single-valued equilibrium is relatively minor, because the sets reduce to points in all generic games.