We analyze group contests over public goods by applying the solution concept of an evolutionary stable strategy (ESS). We show that a global ESS cannot exist, because a mutant free-rider can invade any type of group behavior successfully. There does, however, exist a unique local ESS, which we identify with evolutionary equilibrium. It coincides with Nash equilibrium, the hitherto dominant solution conceptin contest theory, if and only if groups are symmetric. For asymmetric groups it always proposes a different and arguably more sensible solution than Nash equilibrium. We explore the properties of (local) ESS in detail.