The time dependent thermal lensing (TDTL) technique has been used to study collisional energy transfer from highly excited CS2 in baths of Xe, Kf, and Ar, and from highly excited SO2 in Kr and Ar. Bath gas pressures ranged from about 50 to about 600 Torr. The data were analyzed by simulating the observed TDTL signals with a unified hydrodynamic TDTL theory. The results are expressed in terms of [Delta E], the bulk average energy transferred per collision as a function of [E], the mean energy content. The results show that [Delta E] increases dramatically at [E] approximate to 17 500-23 500 cm(-1) for CS2 deactivation, and at [E]approximate to 18 000-22 500 cm(-1) for SO2 deactivation. This enhancement of energy transfer, which was observed previously in NO2 and CS2 deactivation, has been Linked to the presence of nearby excited electronic states. Furthermore, at lower energy, our results reveal an unusual systematic dependence of [Delta E] on bath pressure; energy transfer per collision is significantly more efficient at lower collision frequency. These results and data from the literature can be explained with a phenomenological model which includes collisional vibrational relaxation within each of two sets of vibronic levels, and collision-induced intersystem crossing (CIISC), which exhibits mixed order kinetics.