A method and apparatus for ascertaining the cerebral state of a patient. The method/apparatus may find use in ascertaining the depth of anesthesia of the patient. In one embodiment, the entropy of the patient's EEG signal data is determined as an indication of the cerebral state. A frequency domain power spectrum quantity is obtained from the patient's EMG signal data. The latter quantity can be updated more frequently than the EEG entropy due to its higher frequency. The EEG entropy indication and the EMG power spectrum indication can be combined into a composite indicator that provides an immediate indication of changes in the cerebral state of the patient. In another embodiment, the frequency range over which the entropy of the biopotential signal from the patient is determined is broadened to encompass both EEG signal data and EMG signal data and the entropy so determined used as an indication of the patient's cerebral state.