The non-linear dielectric properties of single crystals of PbMg1/3Nb2/3O3 relaxer ferroelectric were investigated experimentally by using measurements of the dielectric permittivity of this material as a function of the DC bias and the AC driving fields. The results were analyzed using four models of the dielectric response of relaxors currently discussed in the literature, It was shown that among them only one model was consistent with the experimental data. This provides strong evidence that the mechanism of the dielectric response in PMN is controlled by the motion of the interphase boundaries of the polar regions. The analysis of the AC field dependence of non-linear dielectric permittivity showed that this dependence is described by a power law, with a temperature-dependent exponent. With decreasing temperature, the exponent exhibits a crossover, changing from 1 to 2, which is centered around the temperature of the onset of the frequency dispersion of the dielectric permittivity. The crossover was attributed to a change in the pinning regime of the polar region boundaries.