The molecular mobility of the highly asymmetric miscible blend poly(vinyl methyl ether)/polystyrene was investigated by broadband dielectric (frequency range 10(-1)-10(9) Hz) and specific heat spectroscopy (frequency range 10(1)-10(4) Hz). The dielectric spectra revealed a complex molecular dynamic behavior, where three different relaxation processes were observed. At temperatures below the glass transition temperature an alpha'-relaxation was found, with an Arrhenius-like temperature dependence of its relaxation rates. It is assigned to localized fluctuations of the confined PVME segments within a frozen glassy matrix dominated by PS. Above the thermal glass transition temperature two processes with a VFT behavior of their relaxation rates were detected called alpha(1)- and alpha(2)-relaxation, both originating from PVME dipoles fluctuating in PS-rich environments, however with diverse PS concentrations. The relevant length scales for the processes different, corresponding to the Kuhn segment length for the former relaxation and to the CRR for the latter one. The observed multiple glassy dynamics result from spatial local compositional heterogeneities on a microscopic level. Additionally, SHS investigations were performed for the first time for this system, proving an existence of a fourth relaxation process (alpha(3)-relaxation) due to the cooperative fluctuations of both PS and PVME segments. The separation between the thermal alpha(3)-relaxation and dielectric alpha(2)-relaxation increases dramatically with increasing polystyrene concentration, proving that the thermal response is dominated by PS.