Using H-2 NMR and high-precision dielectric spectroscopy, we identified in polybutadiene (PB) at low temperatures (20-100 K) a third relaxation process (gamma-process) in addition to the alpha- and beta-processes. PB samples with different molecular weights (M-w) exhibit a strongly varying relaxation strength (Delta epsilon gamma) though no clear-cut relationship is observed between Delta epsilon gamma and M-w. Concerning the temperature dependence of the gamma-process, the set of samples can be divided into two subsets characterized by different activation energies, where one subset of time constants agrees well with those obtained recently from quasi-elastic light scattering in the melt. From our NMR experiments we conclude that at T < T-g a highly hindered motion (< 8 degrees) is responsible for the gamma-process, which is difficult to explain by typical conformational changes.