A procedure is described which aims to classify an EEG recorded during neurosurgery, for example intracerebral aneurysm clipping. A parametric approach is used; it employs auto-regressive (AR) modelling and Kalman filtering to quantify directly the dynamics of the EEG generating mechanism, supposing it to be a linear, time-invariant system driven by white noise. The results of this EEG processing are analysed together with simultaneous values of arterial blood pressure (ABP) as surgery of this kind is carried out under conditions of controlled hypotension. The object is to compare the sensitivity of ABP data with that obtained from the EEG and so provide an early warning of a potentially dangerous non-physiological state induced by the hypotensive drug (in this case sodium nitroprusside). Some methodological comments on the correct implementation of these algorithms are given and the procedure is compared with similar approaches which have appeared in the literature during the last few years. Particular emphasis is placed on the power spectral analysis of the signal by pointing out a method for spectral decomposition, related to AR power density estimation, which permits the separation of single spectral components in terms of central frequencies and their associated power. Other potential applications of this method are in long term EEG monitoring for the detection of changes due for example to drug infusion, to fast transient events, or to changes in the stationary condition.