The work reported in this thesis comprised two major parts which are: 1) Off-line nonlinear identification of muscle relaxant dynamics, 2) Simulation-based design of a variety of controllers (ranging from classical PID to nonlinear self-tuners) for the closed-loop control of muscle relaxation. Relaxant drugs namely, Vecuronium and Atracurium are considered throughout. Off-line identification studies, using two special nonlinear identification packages (Nonlinear Identification package and Nonlinear Orthogonal Identification package), were carried out to determine nonlinear difference equation models (NARMAX) that best fit (in the least squares sense) recorded data from trials on humans and dogs for each drug. After validation, these models were assumed to represent, in a nonlinear polynomial form, the muscle relaxant drugs pharmacology. Two different approaches were explored for determining the physiological structure of both relaxant drugs: a) The drug model to comprise a pharmacokinetics part to represent the drug distribution, and pharmacodynamics which are often modelled by using the well known Hill equation. b) A cross-correlation approach based on Volterra series. With the relaxant dynamics structure thus fixed, the work proceeded to the control phase. Simple three-term PID controllers were first designed with their parameters being optimised, off-line, using the Simplex method. The non-adaptive nature of this class of controllers makes their robustness open to question when the system parameters for which they have been optimised change. Hence adaptive controllers in the form of linear and nonlinear generalised minimum variance, self-tuners, generalised predictive and nonlinear k-step ahead predictive controllers were also considered. All these latter control approaches are shown to be satisfactory, in terms of transient and steady state performance.