The semiclassical Smatrix theory include ail orders of the interaction recently proposed by Smith et al. for spectral Jine broadening in linear molecules perturbed by atoms is applied to the shifts after inchzion of viirational dephasing effects. Although this theory does not take into accouni the non-commutative character of the interaction at different times, a good consistency betxvcen experimental data and the present calculation is obtained for HCI-Ar and HCLXe at room and lo* temperatures and for the O-O, O-l and O-2 viirational bands. It is shown why the non-commutation of the interaction, which is of major importance for the diatomic-diatomic mciecule case, may be r-uably disrqarded for the diatom-atom case_ 1 _ Introduction In contrast with &e line broadening problem, only a few papers have been devoted to the shift of the vibration-rotation absorption lines. -Although the general form of the line broadening theory also includes the line sift effect, careful attention must be paid to -&e specific aspects of the line shift calculation. The main problem lies in the generally neglected non-commutative character of the interaction at different times previously introduced by Herman [ 11 in a second order treatment with respect to the intermolecular potential Y of the S matrix. This leads to a rotational line shift adding to the vibrational dephasing contribution resuiting from the first order term. This theory has been applied to the calculation of the inert gas pressure-induced shifts of the O-l,