The vibrational relaxation of a system of anharmonic oscillators with high initial vibrational energy into a low-temperature heat bath was studied. It was assumed that the vibration–vibration quasisteady population distribution was instantly established, and during the longer time scale the level population distribution was controlled by a continuous equilibrium vibration–vibration exchange-dominated process or by a vibration–translation exchange-dominated process. Although large differences occurred in upper level populations of the two processes, no significant difference was found in the de-excitation rate. The effect of an-harmonicity did enhance the de-excitation rate in the early stage of the relaxation process. This rate fell off quickly to a value close to the excitation rate obtained for the harmonic oscillator. No large order of magnitude differences in the de-excitation rates of this investigation and previously established excitation rates were found.