This paper deals with the weak Stackelberg strategy in the case of a closed-loop information structure. Two–player differential games are considered with one leader and one follower. We first derive necessary conditions for the Stackelberg equilibrium in the general case of nonlinear criteria for finite time horizon games which lead to an expression of the optimal controls along the associated tra jectory. Then, using focal point theory, the necessary conditions are also shown to be sufficient and lead to cheap control. The set of initial states allowing the existence of an optimal trajectory is emphasized. The Linear Quadratic case is detailed to illustrate these results.