Abstract The possibility is explored of calculating the time evolution of a given initial molecular state, in the presence of sufficiently strong nonadiabatic interactions, with a fully quantum-mechanical approach. Two methods are presented. The first one is based on the determination of the molecular eigenstates, with expansion of the nuclear wavefunctions on a Hermite basis. The second method is based on the Padé 1,1 approximation of the time evolution operator and on a finite difference representation of the time-dependent nuclear wavefunctions. Both methods are applied to simple models of a diatomic molecule.