This paper discusses an analytical technique for calculating the relaxation in time of the electron distribution function f in an environment in which no perturbing forces act on the electrons. For t = 0, f may have any arbitrary form presumed to be caused by perturbing forces which were not zero during t < 0. The technique then allows calculation of the relaxation of f in time for the following types of electron collisions: a) elastic collisions with cold neutrons, b) excitation collisions in which the threshold energy for an elastic excitation collision is small compared to the electron energy, c) ionizing collisions when the energy lost by the electron is small compared to its energy, and d) any combination of the above. In this paper the method is described and simple examples are presented to illustrate the physics of relaxation for the collisional categories listed above. It is pointed out that a number of important problems can be solved by this technique primarily in the area of nuclear EMP: the forrnative lag time problem and the calculation of thermalization time. In addition, the details of the afterglow of extinguished discharges in the monotomic gases can be determined.