We invented a dispersion analysis program that analyzes the relaxation processes from dielectric permittivity based on a combination of the Havriliak–Negami and conductivity contribution functions. By applying the created program to polymers such as nitrile butadiene rubber (NBR) and ethylene propylene diene monomer (EPDM), several relaxation processes were characterized: an α process due to segmental motions of the C-C bond, an α′ process attributed to fluctuations in the end-to-end dipole vector of the polymer chain, the conduction contribution by the filler observed above room temperature, and secondary relaxation processes β and γ of motion for the side group in NBR. In the EPDM specimen, the β process associated with the rotational motion of the side groups, the α process associated with the relaxation of local segmental motion, and the αβ process associated with the origin of the β process at high temperatures above 305 K were observed. The Maxwell–Wagner–Sillars effect and conduction contribution were also presented. The molecular chains responsible for the relaxation processes were assigned by building molecular models of the two polymers. The temperature dependence of the relaxation strength and the shape parameters that characterize the process were investigated. From the temperature-dependent relaxation analysis, the merged αβ process, activation energy, and glass transition temperature were determined and compared.