Supercollisions are collisions in which an inordinate amount of energy (e.g. more than 20 kcal/mol) is transferred in a single collision. Supercollisions were found by experimental and in trajectory calculations and are discussed in the introduction of this paper. In the present work we have calculated values of the collisional efficiency beta by exact solutions of a master equation and the values of the average energy transferred in all collisions (Delta E)(all) and in down collisions (Delta E)(d) with a supercollision double-exponential transition probability and by using the appropriate expressions for average quantities. Mixtures of 0.1% and 0.5% supercollision of 10 000 cm(-1) in weak collision of 300 cm(-1) were studied. Values of beta and (Delta E)(all) were also calculated by using modified known analytical expressions for single-exponential transition probability functions where the (Delta E)(d) quantity of a single exponential is replaced by the value of (Delta E)(d) of a double exponential at the value of the average energy of the reacting molecules. A comparison between the exact and analytical values of beta and (Delta E)(all) shows that the deviations of the analytical from the exact values are small and the former can safely be used in the appropriate pressure and temperature ranges. Results are reported for cyclobutene isomerization to butadiene and cyclobutane fission to ethylene. It is shown that the value of the threshold energy for reaction E(0) (32.2 kcal/mol for the former and 62.7 kcal/mol for the latter) plays a major role in defining the temperature range of the applicability of the analytical expression. In both cases studied, the analytical expression gave good results.