We present a quasielastic neutron scattering (QENS) study of two partially miscible blends : a blend of solution chlorinated polyethylene and poly(methyl methacrylate) (SCPE/PMMA) and a blend of polystyrene and poly(vinyl methyl ether) (PS/PVME). The local dynamics of the ester methyl group in PMMA-d(5) and the ether CH3 group in PVME are investigated as a function of temperature and blend composition. Both the frequency spectra and the intermediate scattering function I(Q,t) are analyzed in detail, and the results are compared with those of the pure polymers. The rotational motion of the ester CH3 group in PMMA-d(5) is sensibly altered by blending with SCPE but no effect is detectable in the PS/PVME system. The time domain data analysis shows that blending broadens the distribution of correlation times in SCPE/PMMA. Results of both homogeneous and phase-separated blends are presented, although no changes in the local dynamics are observed upon phase separation. The difference between the behavior of the two blends is discussed in terms of the lattice model and the intrinsic dynamics of the components.