Knowledge of the absorption of inhalation anaesthetic agents is essential if one is to safely administer them. Despite many years of research in linear science, no model has been described that can reliably predict inhalation agent uptake. To date no published investigation has looked for non¬linearity in the absorption process. The aim if this research project was to determine if the absorption of anaesthetic agents is non-linear, using isoflurane and enflurane as examples. To detect non-linearity, four conditions must be met: <ul> <li>Sensitivity to initial conditions, </li> <li>Fractal Dimension of the attract or, </li> <li>Invariant probability distribution of the attractor, and</li> <li>Detection of an underlying dynamical process. <br></li></ul> Ten measured time series for both isoflurane and enflurane absorption were measured. These were then compared with ten noise signals, with similar standard deviations, means and number of points in the series. Calculated Lyapunov exponents tested sensitivity to initial conditions. The dimension of the attractor was calculated using the following statistics, each giving an approximation of the fractal dimension. Approximate entropy, information entropy, correlation dimension and fractal dimension (box counting method). The Invariant probability distribution of the attractor was tested for using non-linear forecasting. Detection of an underlying dynamical process was determined by the method of surrogate data. Each of the four conditions required have been met with statistical significance ( p< 0.05) and acceptable statistical power (>0.8). It is therefore concluded that the absorption of both isoflurane and enflurane are non-linear processes. The implications and implementations in anaesthesia practice are discussed. / Thesis (PhD (Anaesthesiology))--University of Pretoria, 2005. / Anaesthesiology / unrestricted