The dynamics of miscible blends of poly(p-(hexafluoro-2-hydroxyl-2-propyl)styrene) (PolyHFS) with poly(vinyl methyl ether) (PVME) and poly(2-vinylpyridine) (P2VPy) were investigated via broadband dielectric relaxation spectroscopy (DRS). The HFS moiety forms strong intermolecular associations with proton-accepting polymers, while the steric shielding provided by the two CF3 groups minimizes the number of self-associations. The local, glassy state relaxations of PolyHFS and PVME (or P2VPy) are suppressed in the mixtures due to the strong intermolecular hydrogen bonding. When the number of PolyHFS segments is approximately equal to the number of PVME segments, the local relaxation of PVME is undetectable by DRS. Reduced functional group accessability in P2VPy blends lessens the suppression of local relaxations. A single, broadened dynamic glass transition (a relaxation) is observed for each blend. At temperatures above the alpha process, an additional relaxation is observed, alpha*, which is assigned to the breaking and re-forming of hydrogen bonds as the chain relaxes. The temperature dependence of this process is related to the strength of the hydrogen bonding and the approximate fraction of intermolecularly associated segments.