We describe a six-compartment physiological model of the kinetics and dynamics of induction of anaesthesia with propofol in sheep. It includes a faithful description of initial bolus kinetics caused by accurate representations of the inter-relationships between initial vascular mixing, lung kinetics and cardiac output, the use of the brain as the target organ for propofol anaesthesia (two-compartment sub-model with slight membrane limitation), a description of the effects of propofol-induced changes in cerebral blood flow and a combined description of systemic kinetics as two tissue pools. Variables for the model were estimated from an extensive in vivo data set using hybrid modelling. Propofol was characterized by rapid transit through the lungs, but a slower transit time though the brain, leading to significant delay between arterial blood concentrations and cerebral effects.