Measurements are reported for threshold voltage dependence on the frequency of a nematic liquid-crystalline system composed of cyanophenylcyclohexanes (PCHs). The PCH liquid crystals having a strong dipole only at the terminal position of the molecules showed a frequency independent of threshold voltage at low frequencies. In their mixture, increasing permittivity affected the threshold behavior, finally causing a drop in threshold voltage at low frequencies. The difference in systems with and without the drop in threshold voltage was found to be related to the drift of charge carriers. Relaxation time measurements of transmittance against direct current bias revealed a tendency for the drift of charge carriers in the liquid crystal layer. The liquid-crystalline system composed of PCHs showed relatively slower relaxation than the system with increased permittivity due to addition of certain dopants. In the migration of charge carriers, a model is proposed considering the changes of permittivity. In this model the association structure of the liquid crystal molecules is altered by increasing permittivity. Thus the drift of charge carriers, which is related to the formation of interfacial polarization between the liquid crystal and alignment film layers, is promoted by loss of the molecular association structure.