Segmental dynamics are measured in pure polyisobutylene (PIB), pure deuterium-labeled head-to-head poly(propylene) (hhPP), and a blend containing 70% PIB/30% hhPP by mass using C-13 spinlattice relaxation, 2 H spin-lattice relaxation, and dielectric spectroscopy (DS). The NMR measurements are made between 313 K and 413 K (spin-lattice relaxation measurements are sensitive to motions in the nanosecond range), while the DS measurements (which span the second to microsecond range) are made between 225 K and 325 K. While NMR and DS monitor local dynamics over a wide range of temperature and time, NMR has the additional advantage of being able to determine the local motion of each component in the blend through isotopic labeling. The spin-lattice relaxation data are interpreted using a modified Kohlrausch-Williams-Watts (KWW) correlation function with a Vogel-FulcherTammann-Hesse (VFTH) temperature dependence of relaxation time, giving temperature-dependent segmental correlation times from NMR in the short time (high temperature) range that are compared to dielectric segmental correlation times at lower temperatures. Because of the small PIB dipole moment, DS on hhPP/PIB blends is dominated by the dynamics of hhPP. NMR measurements show very little shift in the component dynamics upon blending, but the shift becomes larger at lower temperatures. One factor in the variation of the separation between the dynamics of the two polymers with temperature is the unusual VFTH parameters for pure PIB, which signify its small fragility. The Lodge-McLeish model is unsuccessful in predicting the changes in component dynamics upon blending for hhPP, while it describes the temperature-dependent dynamics of PIB over the limited temperature range studied by NMR.