Molecular dynamics of miktoarm star copolymers consisting of poly(n-butyl acrylate) PBA and polyethylene oxide (PEO) arms was studied by means of Broadband Dielectric Spectroscopy (BDS) and Nuclear Magnetic Resonance (NMR) methods. The spectroscopic studies were performed for three types of copolymers differing in the composition, namely materials containing 76%, 46% and 16% molar fraction of PBA arms. The local processes, described by the Arrhenius law (e.g. the anisotropic rotation of methyl groups and the anisotropic local motions in the PEO chain), were observed for the studied systems below the glass transition temperature. It was found that the investigated PBA/PEO miktoarm star copolymers are characterized by single glass transition, which may result from similar values of glass transition temperatures of the PBA and PEO polymers. The segmental dynamics in the studied systems was quantitatively described by using the Vogel-Fulcher-Tammann (VFT) relation applied to combined NMR and BDS data. Moreover, above the glass transition temperature the interfacial polarization and conductivity phenomena were detected with the BDS method for all systems under study.