This paper introduces and analyzes sequentially stable outcomes in extensive‐form games. An outcome ω is sequentially stable if, for any ε > 0 and any small enough perturbation of the players' behavior, there is an ε‐perturbation of the players' payoffs and a corresponding equilibrium with outcome close to ω. Sequentially stable outcomes exist for all finite games and are outcomes of sequential equilibria. They are closely related to stable sets of equilibria and satisfy versions of forward induction, iterated strict equilibrium dominance, and invariance to simultaneous moves. In signaling games, sequentially stable outcomes pass the standard selection criteria, and when payoffs are generic, they coincide with outcomes of stable sets of equilibria.