Transport equations are derived in the framework of the rational thermodynamics approach for membrane processes involving a dense (active) polymer layer. The influence of the deformation of the polymer matrix, formation of interacting species, changes in polymer configuration, etc., due to mixing of the penetrant and the polymer can be accounted for in the equations. Studies of permeation fluxes in the transient regime in which the membrane is suddenly put into contact with a solvent can give useful information on the behaviour of polymer-penetrant systems. Experimental results obtained for the transient permeation of alcohols and heptane through different cellulose ester membranes are reported and discussed in the framework of this approach.