The semiclassical initial value representation (SC-IVR), which has recently seen a great deal of interest for treating nuclear dynamics on a single potential energy surface, is generalized to be able to describe electronically nonadiabatic (i.e., multisurface) processes. The essential idea is a quantization of the classical electron-nuclear Hamiltonian of Meyer and Miller [J. Chem. Phys. 70, 3214 (1979)] within the SC-IVR methodology. Application of the approach to a series of test problems suggested by Tully shows it to provide a good description of electronically nonadiabatic dynamics for a variety of situations.