A new semiclassical Formalism has been developed to treat Hamiltonians having explicit time dependence. with particular application to the dissociation of diatomic ions in intense laser fields. Based on this formalism, a hopping algorithm is presented which specifies how classical trajectories should be moved between coupled electronic surfaces. The theory is laid out in a rigorous, general form and an analysis is also presented for tile case where only two electronic surfaces are strongly coupled. In addition, valuable physical insight into the hopping process is obtained by considering the theory in a number of physically relevant limiting cases. From this insight a number of guidelines are proposed which detail the manner in which trajectory hopping should be implemented when lime-dependent potential energy surfaces are present, including the effects of phase coherence and conservation principles.