The statistical theory of pressure broadening is developed for any interaction law in which the potential energy is inversely proportional to some power of the distance between the molecules, including cases in which the forces change sign. This note is intended to prove two propositions: A. When a spectral line is broadened by single impacts of perturbing molecules and the half-width of the line is delta infinity, the statistical theory of broadening is applicable provided delta infinity . R >> 1. In this criterion T is a time comparable to the interval in which the perturbed traverses a distance equal to the impact parameter. B. Far in the wings of a line the statistical theory is always applicable.