An approach which allows for multi-electronic-state dynamics but which is in the spirit of classical molecular dynamics is discussed and applied to both collisional ("curve crossing") and ultrafast optical excitation problems. The formalism seeks to allow for the possibility of quite different nuclear dynamics (e.g., bound vs dissociative) in the different electronic states. The discussion begins from a wave function formulation of the problem, and this enables one to retain interference effects if these are important, but the ultimate objective is to obtain as classical-like a description as possible while taking account of the inter-electronic state coupling. The essential approximation in the method is in the computation of these coupling terms which appear as nonclassical corrections to the classical equations of motion. The computational results are tested against accurate quantal computations, and the agreement is typically quantitative.