In this paper we derive a semiclassical limit of dynamics corresponding to the mapping Hamiltonian formulation of the electronically nonadiabatic problem originally proposed by Stock and co-workers, and Miller and his group. We show results comparing the approach described here with the alternative semiclassical scheme previously used by these workers in applications of this formulation. For simplicity the calculations presented here are for single potential surface models but the approach is generally applicable to many coupled surfaces. We demonstrate by comparison with exact numerical solution that the results obtained with the approach presented here are accurate for arbitrary potential forms but that the alternative semiclassical implementation only apparently converges when repulsive walls in the model surfaces are unimportant.