The analysis of the replicator dynamic in generic perfect information games yields the following results. In the long run, players play a Nash equilibrium provided that initially all strategies are present. There is at most one 'stable' component (formally, an interior asymptotically stable set), play in this component will follow the backwards induction path. Existence of such a component is guaranteed in a simple class of games with at most three consecutive decision nodes. An example of a 'longer' game is provided where some trajectories starting close to the backwards induction component lead away and never come back. (orig.)Available from TIB Hannover: RO 3009(347) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische Informati...