A study is made of the problem of elastic collisions and energy transfer between gases which have separate Maxwellian velocity distributions. It is shown that the expression for the energy transfer rate obtained by Desloge(1) for gases of arbitrary temperature and particle mass can be adapted into a convenient form which involves a ratio of particle masses, the difference in the gas thermal energies, and a collision frequency for energy transfer. An analysis is then made of the collision frequency in terms of an average momentum transfer cross section which is defined for conditions of thermal nonequilibrium. The general equations are next specialized to consider the problem of elastic electron collisions in heavy particle gases. To obtain useful numerical expressions for electron-neutral particle collision frequencies and energy transfer rates, an analysis has been made of the momentum transfer cross sections for N2, O2, O, H and He. Calculations have also been made of the Coulomb momentum transfer cross section, collision frequency, and energy transfer rate.