Objective. Resting electroencephalographic activity is typically indistinguishable from a filtered linear random process across a diverse range of behavioural and pharmacological states, suggesting that the power spectral density of the resting electroencephalogram (EEG) can be modelled as the superposition of multiple, stochastically driven and independent, alpha band (8-13 Hz) relaxation oscillators. This simple model can account for variations in alpha band power and '1/f scaling' in eyes-open/eyes-closed conditions in terms of alterations in the distribution of the alpha band oscillatory relaxation rates. As changes in alpha band power and '1/f scaling' have been reported in anaesthesia we hypothesise that such changes may also be accounted for by alterations in alpha band relaxation oscillatory rate distributions.Approach. On this basis we choose to study the EEG activity of xenon and nitrous oxide, gaseous anaesthetic agents that have been reported to produce different EEG effects, notable given they are both regarded as principally acting via N-methyl-D-aspartate (NMDA) receptor antagonism. By recording high density EEG from participants receiving equilibrated step-level increases in inhaled concentrations of xenon (n= 24) and nitrous oxide (n= 20), alpha band relaxation rate (damping) distributions were estimated by solving an inhomogeneous integral equation describing the linear superposition of multiple alpha-band relaxation oscillators having a continuous distribution of dampings.Main results. For both agents, level-dependent reductions in alpha band power and spectral slope exponent (15-40 Hz) were observed, that were accountable by increases in mean alpha band damping.Significance. These shared increases suggest that, consistent with their identified molecular targets of action, xenon and nitrous oxide are mechanistically similar, a conclusion further supported by neuronal population modelling in which NMDA antagonism is associated with increases in damping and reductions in peak alpha frequency. Alpha band damping may provide an important link between experiment and theories of consciousness, such as the global neuronal network theory, where the likelihood of a globally excited state ('conscious percept'), is inversely related to mean damping.