The paper discusses a class of bilevel optimal control problems with optimal control problems at both levels. The problem will be transformed to an equivalent single level problem using the value function of the lower level optimal control problem. Although the computation of the value function is difficult in general, we present a pursuit-evasion Stackelberg game for which the value function of the lower level problem can be derived even analytically. A direct discretization method is then used to solve the transformed single level optimal control problem together with some smoothing of the value function.