This paper presents the results of a study of polymer films based on a blend of low-density (high-pressure) polyethylene (LDPE, HPP) with a copolymer of ethylene and vinyl acetate (EVA, sevilen). The use of thermal activation, infrared and dielectric spectroscopy methods made it possible to describe the electric charge relaxation processes in the polymer blends investigated. The data obtained suggested the presence of an α-relaxation process in the samples in the temperature range 250–280 K. An increased value of the activation energy of this process was also found in the LDPE/EVA samples compared to that in the LDPE one. This effect has been interpreted as the appearance of deeper traps of charge carriers in the blends. The dependences obtained by dielectric spectroscopy indicated the presence of hopping conductivity in the subjects of research.