The permeation of CO2, O-2, N-2, and CH4 through composite membranes consisting of poly(dimethylsiloxane) (PDMS) substrates coated with fluorine rich plasma polymers was studied. Measurements were made with different thicknesses of plasma polymer (0 to 1 mu m) and at different temperatures between 35 and 75 degrees C, which allows us to determine the permeability coefficients and permeation activation energies of each layer. The results are compared to a simple resistance in series permeation model. For CH4 and N-2 the permeabilities of the composite membranes deviate from the resistance in series model. This is most likely due to plasma modification of the PDMS surface during the early stages of plasma polymerization.