The pore structures of adsorbents such as zeolites and metal-organic frameworks comprise regular arrays of uniform channels of molecular dimensions, thus offering the possibility of size selective (molecular sieve) separations. Molecular sieve separations have traditionally been carried out in a cyclic batch adsorption/desorption process but, in principle, a steady state membrane process would be an attractive alternative. Considerable success has been achieved at the laboratory scale for several different molecular sieve separations but the difficulty of fabricating, on a large scale, a sufficiently coherent and robust zeolite membrane has largely prevented the commercial application of such processes. Selected examples of kinetic separations are presented in order to illustrate some of the features of such systems.