Thermoplastic vulcanizates (TPVs) are a special class of polymer blends comprised of a thermoplastic polypropylene (PP) matrix and a dynamically vulcanized ethylene propylene diene monomer (EPDM) rubber. Due to the presence of crosslinked rubber particles, TPVs exhibit complex rheological fingerprints similar to those of soft elastic solids. In this study, we attempt to draw a correlation between the rheology of several TPVs to the base components, namely, PP and EPDM. The effects of long chain branching of the primary constituents (prior to crosslinking), the level of curing, and the amount of crosslinked rubber on their rheology are studied in detail and found to affect the rheology to various degrees. All TPVs studied exhibited a universal relaxation modulus of the form ( G ( t ) − G y ′ ) ∝ t − p, where G y ′ is the equilibrium modulus indicating the elastomeric nature of TPVs (increases with the rubber crosslink density) and the absence of terminal relaxation with a proportionality constant dependent on the constituent polymer combination, the level of curing, and rubber concentration. At high deformations, these complex materials yield in both shear and extensional flows, and relevant stresses are determined and compared. While yield stress in shear can be easily determined, for the first time the yield stress in extension is observed and reported for polymer melts.