A new experimental protocol based on the measurements of sorption (S), desorption (D), resorption (RS), and redesorption (RD) has been used to study the molecular transport of aliphatic alkanes through the miscible blends of an ethylene-propylene random copolymer and an isotactic polypropylene over the temperature interval 25-70 degrees C. Diffusion and activation parameters are evaluated and their dependencies on solvent size, shape, and nature are discussed. Estimated values of the molar mass between chain entanglements, kinetic rate constants, and overshoot index parameters have been influenced by the polymer-solvent interactions. The sorption-diffusion mechanism is found to be of anomalous type.