A high-pressure research on rapeseed oil and mixtures of rapeseed oil with methyl alcohol has been made. In all cases, at least one occurrence of the first order phase transition similar to that in castor oil was noticed [R.M. Siegoczyński, Reports of the Institute of Physics. No. 46, Publishing House of the Warsaw University of Technology (1998)]. Experiments were performed in a cylindrical chamber with a simple piston system, working together with 20 ton hydraulic laboratory press. The pressure in those experiments was approaching 1 GPa. Changes of pressure, volume, temperature and capacitance were recorded using an advanced data acquisition system. In this article, the changes of the relative electric permittivity ϵr as function of pressure and also the compressibility of investigated liquids have been presented. Abnormal rise of the dielectric constant in the mixture of rapeseed oil with methyl alcohol was observed. These results suggest the occurrence of a new phase transition apart from the one observed earlier in rapeseed oil [A.J. Rostocki, R. Wiśniewski and T. Wilczyńska, J. Mol. Liq., in press].