We introduce a contest model with multiple rounds where only the contestants who exert most effort qualify for the next round. Moreover, a subset of these contestants receives a prize in each round. If each round features more qualification spots than prizes and the order of valuations is constant across rounds, equilibrium behavior in each round is equivalent to the behavior in a one-shot, multi-prize all-pay auction. Otherwise, equilibrium behavior can be influenced by a novel type of identity-dependent externality. We derive a closed-form solution for cases with three contestants and two rounds. In these cases, the dynamic contest outperforms the corresponding static contest in terms of expected effort.