The effect of non-adiabatic vibronic transitions between crossing vibronic terms on the vibrational deactivation of diatomic molecules by atoms, when one of the partners is in degenerate electronic state is discussed. The consideration is based on an approximate method for calculating asymptotic adiabatic electronic terms for such systems. This method takes into account both Coulomb and exchange interactions. Calculations performed for the systems O2+ O, N2+ O, CO + Fe, NO + Ar show that the inclusion of nonadiabatic transitions greatly improves the agreement between theory and experiment.