We report chemical shift measurements of the hydroxyl protons in methanol and ethanol up to 450 degrees C and over a wide range of pressures. The extent of hydrogen bonding compared to room temperature conditions is obtained for the alcohols. The results are compared with our previously reported ones for water. Surprisingly, all three substances show very similar behavior when compared on the basis of reduced thermodynamic variables. Compared to the room-temperature situation, an extent of hydrogen bonding eta of about 30% prevails for all three substances at near-critical conditions. The density-reduced extent of hydrogen bonding eta/rho* reveals that the alcohols form hydrogen-bonded aggregates already at low, gaslike densities. The temperature dependence of the data, extrapolated to a constant liquidlike density, implies enthalpies of hydrogen bonding of 12.8 and 16.8 kJ/mol in methanol and ethanol, respectively.