Differential thermal analysis (DTA) measurements under pressures up to 250 MPa and temperatures of about 300 to 370 K have been performed on long chain n-alcohols C nH2 n + ,OH, including I-tetradecanol, I-pentadecanol, I-hexadecanol, I-heptadecanol and I-octadecanol. On heating, these alcohols change from a crystalline to a rotator phase a few degrees below their melting points. The rotational state of I-tetradecanol can only be reached by cooling from the melt. The p-Tphase diagrams of these alcohols have been established. They demonstrate, that the coexistence region of the rotator phase is increased under pressure. In contrast to the high-pressure phase behaviour of long chain n-paraffins the phase transition lines of n-alcohols diverge upon increasing pressure and no triple point is observed. This different behaviour is connected with the enlarged enthalpy change at the transitions to the rotator phase that reduces the slope dT/dp of this phase transition line. Dielectric measurements were performed on I-pentadecanol which support the orientationally disordered state of the rotator phase.