Dielectric spectroscopy was carried out to measure the alpha-relaxation (local segmental motion) and the higher frequency, secondary relaxation (beta-mode) in 1,4-polybutadiene, both neat and containing a nonpolar diluent, mineral oil. The a-relaxation shifted to lower frequencies (antiplasticization) in the presence of the diluent, suggesting the glass temperature of the latter is higher than the T-g of the polymer (i.e., >187K). The T-g of neat mineral oil cannot be determined directly, due to crystallization. While the diluent increased the magnitude of the alpha-relaxation times, it had no effect on the beta-relaxation. Moreover, neither the shape of the alpha-relaxation function nor its temperature dependence was influenced by the diluent. From this we conclude that the main effect of the mineral oil was to increase the local friction, without changing the degree of intermolecular cooperativity of the molecular motions. We also find that near the glass temperature, there is rough agreement between the time scale of the secondary relaxation process and the value of a noncooperative relaxation time estimated from theory. This approximate correspondence between the two relaxation times also holds for 1,2 polybutadiene. However, the beta-process cannot be identified with the noncooperative alpha-relaxation, and the relationship between them is not quantitative.