Using the Boltzmann equation, the initial filling rate of the high-energy tail of the distribution function is calculated for the case where the distribution function is zero above, and Maxwellian below a cutoff point. A general expression is obtained for the filling rate, as well as for the depletion rate of the distribution function below the cutoff point. The results are applied to hard sphere molecules, for which they can be evaluated analytically in terms of error functions. The resulting growth rate is compared with the corresponding one obtained using the Bhatnagar—Gross—Krook collision term. The latter rate correctly shows a number of aspects of the qualitative behavior, but is quite different numerically. The general result is also applied to Coulomb molecules, and the character of the resulting divergencies is exhibited. Relaxation of the distribution function in time is studied with the aid of a high-speed computer. It is concluded that under all conditions of physical interest, the characteristic filling time for the tail of the distribution function is of the order of the mean time between collisions.