A globally uniform time-independent semiclassical wave function for nonadiabatic scattering is presented. This wave function, which takes the form of a surface-hopping expansion, is motivated by the globally uniform semiclassical wave function of Kay and co-workers for the single-surface case. The surface-hopping expansion is similar to a previously presented primitive semiclassical wave function for nonadiabatic problems. This earlier wave function has the important feature that it correctly incorporates all phase terms, allowing for an accurate treatment of quantum interference effects. The globally uniform expression has important numerical advantages over the primitive formulation. The globally uniform wave function does not have caustic singularities, and the globally uniform calculation avoids a root search for trajectories obeying double-ended boundary conditions that is required by the primitive semiclassical calculation. (C) 2004 American Institute of Physics.