The so-called thermoplastic vulcanizates (TPV) are essentially blends of a crystalline thermoplastic polymer (e.g., polypropylene) and a vulcanizable rubber composition, prepared through a special process called dynamic vulcanization, which yields a fine dispersion of micron-size crosslinked rubber particles in a thermoplastic matrix. Such materials are by nature complex polymer systems, i.e., multiphase, heterogeneous, typically disordered materials for which structure is as important as composition. Correctly assessing their rheological properties is a challenging task for several reasons: first, even if the uniformity of their composition is taken for granted, TPV are indeed very complicated materials, not only heterogeneous but also with a morphology related to their composition; second, their morphology can be affected by the flow field used; third, the migration of small labile ingredients (e.g., oil, curative residue, etc.) can in the meantime significantly change the boundary flow conditions, for instance through self-lubrication due to phase separation of the oil, or wall slip, or both. The aims of the work reported were to investigate a series of commercial TPV through the so-called Fourier transform rheometry, a testing technique especially developed to accurately investigate the nonlinear viscoelastic domain. Results are tentatively interpreted in terms of material composition and structure.