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Controlling the level of anaesthesia is important for improving the success rate of surgeries and for reducing the risks to which operated patients are exposed. This paper proposes a nonlinear H-infinity approach to optimal control of the level of anaesthesia. The dynamic model of the anaesthesia, which describes the concentration of the anaesthetic drug in different parts of the body, is subjected to linearization at local operating points. These are defined at each iteration of the control algorithm and consist of the present value of the system's state vector and of the last control input that was exerted on it. For this linearization Taylor series expansion is performed and the system's Jacobian matrices are computed. For the linearized model an H-infinity controller is designed. The feedback control gains are found by solving at each iteration of the control algorithm an algebraic Riccati equation. The modelling errors due to this approximate linearization are considered as disturbances which are compensated by the robustness of the control loop. The stability of the control loop is confirmed through Lyapunov analysis. [ABSTRACT FROM AUTHOR]