This work presents composite membranes comprising poly(acrylonitrile) (PAN) as the support and polydimethylsiloxane (PDMS) as the selective top layer. For sunflower oil/hexane and polyisobutylene (PIB)/hexane, the permeation characteristics of these membranes for various feed concentrations and pressures are studied. For each system, the effect of transmembrane pressure upon the flux and retention of the PAN/PDMS composite membrane is investigated. Osmotic phenomena similar to those of aqueous systems are observed and interpreted using the van¿t Hoff equation. The hexane flux increases linearly with the applied pressure and the solution-diffusion model seems to describe satisfactory the aspects of its transport to these systems. The hexane permeability decreases with the increase of the feed concentration. Its normalization by the viscosity inside the swollen membrane (according to the Stokes¿Einstein diffusion phenomenon) and the swelling degree of the membrane results in a constant value quantifying the hexane transport independent of the solute present in the feed mixture. The flux of the solute (oil or PIB) increases linearly with the applied pressure as well, especially at low feed concentrations when the membrane swelling is higher, indicating coupling of solute transport to solvent flux. For the same feed solution concentration, the effect of flux coupling (solvent-induced solute dragging) decreases with the molecular weight of the solute. Ultimately, when the applied pressure increases; the increase of hexane flux is much higher than the corresponding solute (oil or PIB) flux resulting to an increase of the membrane retention.