Results are presented of studies on the low frequency (f' 250 kHz) non-linear dielectric effect on approaching the nematic and smectic A phases in 4′-cyano-4-n-alkylbiphenyls (nCB, for n = 6, 7, 8, 10, 11, 12). In all cases, the mean-field behaviour was valid up to the clearing temperature. In the case of the isotropic-nematic transition (6CB, 7CB, 8CB), a quantitative agreement with the relation based on the Landau-de Gennes model was also ascertained. The specific feature of the research method applied was that the characteristic time introduced by the measurement field (T′ ≊ 1/f) was always greater than the relaxation time τ, i.e. the condition: (T′/τ)>1 was satisfied up toTc.