The permeability of helium cross a composite membrane derived from six monolayers of 5,11,17,23,29,35-hexaamidoxime-37,38,39,40,41,42-hexakis(1-octyloxy)calix[6]arene (1) and poly[1-(trimethylsilyl) 1-propyne] cast film has been found to be significantly reduced when the film is exposed to moisture. In sharp contrast, the permeability of nitrogen across this same composite was unaffected by moisture. These results, by themselves: provide compelling evidence for the existence of two distinct pathways for diffusion: one that strongly favors the transport of He over N-2,and a second that is much less selective. Unusual pressure effects that have been observed for the normalized flux Of He support a model in which this smaller permeant can diffuse through individual calix[6]arenes.