Abstract The transport of liquids into semicrystalline thermoplastic resins such as poly(aryl ether ether ketone) (PEEK) is an extremely complex process, markedly dependent upon the temperature, crystallinity and concentration of the penetrant at the surface. Similarities and differences in the sorption, desorption, resorption, swelling and solvent-induced crystallinity of toluene and carbon disulfide into amorphous and semicrystalline PEEK are reported. The transport of these two liquids into PEEK illustrates many of the complexities associated with non-Fickian diffusion: sharp penetration front, slow relaxation processes, solvent-induced crystallinity and anisotropic swelling and deswelling. Desorption is a two-step process in which 30–50% of the penetrant is rapidly desorbed in a few hours. The rate of CS 2 sorption and desorption is much greater than that of toluene. The rate of resorption is significantly less than that of the initial sorption but the desorption process is essentially unchanged.