The precise mechanisms underlying general anæsthesia pose important and still open questions. To address them, we have studied anæsthesia induced by the widely-used (intravenous) propofol and (inhalational) sevoflurane anæsthetics, computing cross-frequency coupling functions between neuronal, cardiac, and respiratory oscillations in order to determine their mutual interactions. The phase domain coupling function reveals the form of the function defining the mechanism of an interaction, as well as its coupling strength. Using a method based on dynamical Bayesian inference, we have thus identified and analyzed the coupling functions for six relationships. By quantitative assessment of the forms and strengths of the couplings, we have revealed how these relationships are altered by anæsthesia, also showing that some of them are differently affected by propofol and sevoflurane. These findings, together with the novel coupling function analysis, offer a new direction in the assessment of general anæsthesia and neurophysiological interactions in general.