We have studied the equilibration dynamics of liquid water and alcohols following a local deposition of energy using time-resolved femtosecond mid-infrared pump-probe spectroscopy. The equilibration dynamics is monitored via the spectral response of the OH-stretch vibration. It is found that the equilibration leads to complicated changes of the absorption band of the OH-stretch vibration including a shift of the absorption band and a decrease of the absorption cross section. Interestingly, these spectral changes do not occur simultaneously, which indicates that they are associated with the equilibration dynamics of different low-frequency modes. For water, we find an equilibration time constant of 0.55 +/- 0.05 ps. We observe that the equilibration time strongly increases going from water to alcohols such as methanol, ethanol, and propanol which means that water molecules can adapt much faster to a local deposition of energy than other hydrogen-bonding liquids.