For sleep classification, automatic electroencephalogram (EEG) interpretation techniques are of interest because they are labour saving, in contrast to manual (visual) methods. More importantly, some automatic methods, which offer a less subjective approach, can provide additional information which it is not possible to obtain by manual analysis.;An extensive literature review has been undertaken to investigate the background of automatic EEG analysis techniques. Frequency domain and time domain methods are considered and their limitations are summarised. The weakness in the R & K rules for visual classification and from which most of the automatic systems borrow heavily are discussed.;A new technique - model based dynamic analysis - was developed in an attempt to classify the sleep EEG automatically. The technique comprises of two phases, these are the modelling of EEG signals and the analysis of the model's coefficients using dynamic systems theory. Three techniques of modelling EEG signals are compared: the implementation of the non-linear prediction technique of Schaffer and Tidd (1990) based on chaos theory; Kalman filters and a recursive version of a radial basis function for modelling and forecasting the EEG signals during sleep. The Kalman filter approach produced good results and this approach was used in an attempt to classify the EEG automatically. For classifying the model's (Kalman filter's) coefficients, a new technique was developed by a state-space approach. A 'state variable' was defined based on the state changes of the EEG and was shown to be correlated with the depth of sleep. Furthermore it is shown that this technique may be useful for automatic sleep staging. Possible applications include automatic staging of sleep, detection of micro-arousals, anaesthesia monitoring and monitoring the alertness of workers in sensitive or potentially dangerous environments.