Calculations are made of the quasi-molecular emission spectra formed in thermal collisions of Ca(4s4p, P-1, 4s3d, D-1) and He(1s(2), S-1(0)) atoms. The calculations are made within the framework of Demkov model [1] and in the trajectory approach on rectilinear trajectories and in the quasi-static approximation. It is shown that the Demkov model can be used for the description of the spectrum even in the case where nonadiabatic transitions are absent or negligibly weak. A rapid variation of the quasi-molecular radiative width leads to the formation of a peak in the spectrum, which is shifted to the blue wing with respect to the position of the forbidden 3(1)D --> 4(1)S(0) atomic transition. (C) 2000 MAIK "Nauka/Interperiodica".