Supersonic molecular beams may be isolated from gas which has been allowed to expand through a nozzle. This paper concerns the kinetic theory of the isolation of such beams, taking into account the effect of collisions in the region between the skimmer and the collimator. These collisions turn out to be important. In particular, they offer an explanation of two interesting phenomena: (a) the existence of a maximum beam intensity as the distance is varied between the nozzle and the collimating system and (b), in a mixed beam, large increases in the intensity of the heavy gas as its initial concentration is reduced by replacement with a much lighter gas. The theory is compared with various experimental results. Although severe approximations have been introduced into the theory, it appears to predict the above phenomena in a way that is better than qualitative.