Calculations are reported for collisionally induced emission spectra of Ca(4s4p ³P₁, ³P₂) and Mg(3s3p ³P₁, ³P₂) - He(1s^{2 1}S₀) quasi-molecules. The calculations were made in the quasi-static approximation and on the basis of the Demkov model. The shape of a spectral line depends on the parameter of nonadiabaticity and the fact whether an initial populated state was of the radiative or the forbidden type. The dynamic approach supported the formation of a satellite shifted from the position of the forbidden atomic transition to the blue wing in the case where the energy of the radiative atomic transition is lower than the energy of the forbidden transition.