The nonlinear dielectric effect (NDE) measurements of nonanol, undecanol, and dodecanol in the vicinity of the melting point were performed to examine and to develop the hypothesis on pretransition phenomena in decanol (Pocheć et all, J. Phys. Chem. C 2019, 123, 16929–16933). The results show that the anomalous increase of the nonlinear dielectric effect in the immediate vicinity of the melting point is uniform for each of the studied compounds. We link the observed anomaly with the formation of a liquidlike film on the surface of the solid. The scaling function describing these anomalies was proposed and tested. We proved the feasibility of NDE studies in the examination of premelting phenomena.