We demonstrate the applicability of the time-dependent semiclassical initial-value formalism to the problem of population transfer between adiabatic potential surfaces which are coupled through a pulsed laser field. Despite the fact that solutions of highly nonlinear classical equations are entering the semiclassical expression, our results for ultrashort pulse excitation are in good agreement with full quantum solutions. Even in the case where the Rosen-Zener approach to population transfer breaks down, the semiclassical results are still close to the quantum ones. [S1050-2947(99)06609-3].