Solid–liquid equilibria, (SLE) of n-alkanes (n-octadecane, or n-eicosane) + methyl 1,1-dimethylethyl ether (methyl tert-butyl ether) at very high pressures up to about 1.0 GPa have been investigated in the temperature range 313 K to 353 K using a new thermostatted apparatus for the measurement of transition pressures from the liquid to the solid state in two-component isothermal solutions. The freezing and melting temperatures at a constant composition increase monotonically with pressure. The high pressure devices used are briefly described and experimental results obtained in isothermic (T = constant) conditions, p–x, are interpolated to well known T–x diagrams. The solid–solid first order transition, characteristic for n-alkanes, shifts to a lower temperature with increasing pressure. In order to describe the pressure–temperature–composition relation of high-pressure SLE, the Nagaoka–Makita polynomial was satisfactorily used.