Approximate entropy (ApEn) and Lempel-Ziv complexity (LZC), which are nonlinear quantification methods of the regularity of electroencephalogram (EEG) signals, have recently been proposed as measures of the depth of anaesthesia. The present study compares these two methods to two traditional linear methods, namely 95% spectral edge frequency (SEF95) and median edge frequency (MEF), and a commercial method, bispectral index (BIS), in pre-anaesthesia, maintenance, and recovery stages. Twenty-three patients (12 males and 11 females) with inhalational anaesthesia were enrolled. The BIS, SEF95, and MEF data of the anaesthetized subjects are collected using a BIS monitor. Raw EEG data are transmitted to a computer for off-line analysis to obtain ApEn and LZC values. The ApEn, LZC, SEF95, and MEF values are converted to a 0-100 range for comparison with BIS. There are significant differences (P < 0.05) in th results between the pre-anaesthesia and maintenance stages and between the recovery and maintenance stages obtained from BIS, ApEn, and LZC, which indicates that the three measures can differentiate the state of anaesthetia in a patient. There are no differences (P > 0.05) in the ApEn and LZC values between the pre-anaesthesia and recovery stages, indicating that ApEn and LZC show the increases in values from maintenance phase to recovery phase similar to the reductions in values from pre-anaesthesia phase to maintenance phase. The changes of ApEn and LZC in recovery stage are significantly larger than that exhibited by BIS. BIS shows a statistically reduced level from the pre-anaesthesia to the recovery stage, whereas ApEn and LZC show no difference. This indicates that ApEn and LZC respond more rapidly to recovery than does BIS. LZC and ApEn perform more sensitively than BIS in detecting the recovery of consciousness from non-responding to responding. Moreover, traditional assessments SEF95 and MEF perform poorly compared to BIS.