A process for the removal of at least one non-water vapor component of a vaporous mixture, the basic process comprising directing a vaporous mixture against the feed side of a membrane, directing a condensable vapor sweep stream past the permeate side of the membrane in a manner such that the flow of the condensable vapor sweep is substantially countercurrent to the flow of the vaporous mixture, thereby transporting at least a portion of at least one non-water vapor component of the vaporous mixture from the feed side to the permeate side of the membrane to form a combined permeate side mixture of condensable vapor and at least one non-water vapor transported component.