The effect of resonant charge exchange collisions between an initially monoenergetic unipolar ion stream and a uniform neutral background gas is investigated by postulating a simplified collision mechanism. First‐order approximation to the velocity distribution function for distances small compared to the mean free path and an asymptotic distribution function for large distances are obtained; both are found to be highly anisotropic. The results are valid if the ion energy gained between subsequent collisions is large compared with the thermal energy of the neutral gas. Errors introduced by the physical assumptions are discussed.