A general method is given for solving Boltzmann's equation for the steady-state velocity distribution of electron-ion gases, such as those present in gaseous nebulae or stellar atmospheres. In a typical plane- tary nebula it is found that the velocity distribution is very close to Maxwellian. Because the average lifetime of an electron in the assembly is about 10 years and because its energy is reshuflied nearly every second by electrostatic encounters, the deviations from the equilibrium Maxwellian distribution must be very small. The non-Maxwellian distributions obtained by Hagihara are merely first approximations to an expansion of a Maxwellian distribution in terms of the wrong temperature. Section I gives a general summary of the results and the physical picture behind them. Section II lists the formulae for the probabilities of all processes involved; in Section III Boltzmann's equation is set down, and Hagihara's work is discussed. Section TV gives a general method for solving Boltzmann's equation when electrostatic interaction is the dominating term