The dielectric behavior of polybutadiene copolymers with different compositions of 1,2 and 1,4 units is analyzed to study the influence of the microstructure on the relaxation spectrum, especially the beta relaxation. The experimental data were obtained between 10(-2) and 10(6) Hz and temperatures above and below T-g. Above Tg, the relaxation spectra are described by the superposition of two processes, the main a relaxation at low frequencies and a beta relaxation at high frequencies. The a relaxation has the typical Vogel-Fulcher-Tammann behavior and exhibits a quasi-linear shift of time scale upon change of the vinyl content. The high-frequency process shows Arrhenius behavior only in the case of the homopolymers. For the other samples with a mixture of microstructures, spectral broadening occurs and deviation from the Arrhenius behavior is observed. In these samples, the relaxation can be modeled by the simple assumption that the high-frequency process consists of a superposition of two separate processes, each with the properties of the beta relaxation of one of the homopolymers. This suggests that secondary relaxations can relax quite independently from the segmental relaxation and are therefore restricted to a very local environment influenced by intramolecular interaction.