The form of accurate semiclassical surface hopping propagators and wave functions for processes involving more than one electronic quantum state is discussed. It is shown that conditions, which define the required non-classical events along trajectories, can be derived from the Schrödinger equation. These conditions also uniquely specify the direction of the momentum change accompanying the energy conserving hops between electronic energy surfaces and the amplitudes associated with these hops. Transition probabilities obtained from surface hopping calculations on model systems are presented for classically allowed and classically forbidden transitions, and these results are compared with exact quantum calculations.