By means of quasielastic neutron scattering, we have investigated the dynamics of two polymers, head-to-head poly(propylene) (HHPP) and poly(ethylene-propylene) (PEP), through the incoherent scattering function of hydrogens, i.e., the H self-correlation function. Backscattering techniques have allowed us to cover mesoscopic time scales in the momentum transfer region 0.2 <= Q <= 1.8 angstrom(-1). For both polymers, the glassy dynamics below the glass-transition temperature T-g (HHPP: T-g = 248 K; PEP: T-g = 213 K) is dominated by the methyl group rotations. In the temperature region investigated in the supercooled liquid state-well above the glass transition-we have observed a qualitatively similar behavior for both systems: anomalous sublinear diffusion with deviations from Gaussian behavior in the high-Q range. Because of the differences in T-g, the time scales associated with HHPP are slower than those observed for PEP in this regime. These results have been taken as reference to address the question of the dynamic miscibility in the blend system composed by a mixture of 50% HHPP/50% PEP. Exploiting isotopic labeling, we could experimentally isolate the HHPP-component dynamics in the blend by using a mixture of protonated HHPP and deuterated PEP. In the glassy state, we found that the methyl group dynamics of HHPP is not affected by blending. On the other hand, well above the average glass transition of the blend, the hydrogen motions in HHPP become faster in the presence of PEP. The combined analysis of these results and measurements on the fully protonated blend allowed us finally to deduce also the PEP-component dynamics in the blend in the supercooled liquid state. This dynamics is slowed down by blending but remains faster than that shown by the HHPP component in the blend. These results are discussed in the light of a recent model for blend dynamics proposed by Lodge and McLeish based on the concept of self-concentration. The experimentally observed behavior is well predicted by such a model in the Q and temperature range investigated well above the glass transitions of the polymers.