This paper investigates the use of autoregressive (AR) model order estimation criteria for monitoring awareness during anaesthesia. The Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC) were applied to electroencephalogram (EEG) data from 29 patients, obtained during surgery, to estimate the optimum multivariate AR model order. Maintenance of anaesthesia was achieved with propofol, desflurane or sevoflurane. The optimum orders estimated from the BIC reliably decreased during anaesthetic-induced unconsciousness, as opposed to AIC estimates, and, thus, successfully tracked the loss of awareness. This likely reflects the decrease in the complexity of the brain activity during anaesthesia. In addition, AR order estimates sharply increased for diathermy-contaminated EEG segments. Thus, the BIC could provide a simple and reliable means of identifying awareness during surgery, as well as automatic exclusion of diathermy-contaminated EEG segments.