The first rigorous kinetic theory of ion mobility in neutral gases, valid for electric fields of arbitrary strength without restriction on the ion-neutral mass ratio or interaction potential, is presented. The theory is based on the use of a set of basis functions in which the ions are allowed to have a temperature different from that of the neutral gas. The convergence of a series of approximations for the mobility is good, and the resulting expressions are not expansions in powers of the field strength. In lowerst approximation, the equation for the mobility is nearly the same as that obtained from an approximate free-flight theory, except for the appearance of an effective temperature in the diffusion, or momentum-transfer, collision integral. This difference is the crucial point that allows experimental measurements of ion mobility as a function of field strength to be used to obtain information on ion-neutral potentials. Data on K + ions in He, Ne, and Ar are analyzed as an example; the range of effective temperatures is approximately 100 to 20,000°K. At high effective temperatures the results agree with similar information obtained from the scattering of ion beams in gas targets.