We investigate the influence of two groups of ions on the complex dielectric constant of a nematic liquid crystal limited by perfectly blocking electrodes. The analysis is performed by solving the equations of continuity for the two groups of cations and anions, and the equation of Poisson relating the actual electric field to the net density of charge. We consider a typical experiment of impedance spectroscopy, and evaluate the equivalent resistance and reactance of the cell, in the series representation, versus the frequency of the applied voltage to the cell. We show that the presence of two groups of ions gives rise to two plateaux in the spectrum of the resistance, similar to those related to the ambipolar and free diffusion in the case where there is only one type of ions, but for which the cations and anions have different diffusion coefficients. The correspondence between the usual ambipolar and free diffusion coefficients and those related to the presence of two groups of ions is discussed, The spectra of the real and imaginary parts of the complex dielectric constant are obtained, and their dependence on the bulk densities of the two types of ions is investigated. The nonvalidity of the superposition principle is discussed.