Anaesthetic drugs with a rapid onset of action and a short half-live, such as the hypnotic propofol and the analgesic opioid remifentanil, allow easy control of the anaesthetic depth and noxious stimuli associated to surgical interventions, and reveal most of the potential of target controlled infusion for general anaesthesia. Furthermore, mathematical models were incorporated in microcomputers in delivery system devices, calculating the drug concentrations in the blood and brain, according to the infusion rate. This book approaches the characteristics of propofol and remifentanil that allow the fast emergence of target controlled infusion for general anaesthesia, and its potential for closed loop control anaesthesia.