A comprehensive mathematical model of the respiratory system is developed using available physiological data and structural information. The model evolves through systemic analysis and development of causal relationships describing the three main subsystems; neural control, lung mechanics and gas exchange. The subsystem models are based upon physiological evidence where possible but limited experimental data necessitates some structural hypothesisation particularly in the neural control model where knowledge concerning the central respiratory centre is scant and vague. Investigation of the neural system employs the concept of maintained respiratory rhythmicity through two coupled oscillators. Software and hardware models are generated and implemented and comparative testing gives a better understanding of the system behaviour. An improved model of the lung mechanics system is developed incorporating the concept of the equipressure point and a new theoretical approach to aid analysis. Performance of new experiments on humans allows further validation of a suitably adapted, existing gas exchange model. Detailed analysis and validation of the individual subsystem models using appropriate performance criteria, and their subsequent combination through the design of physiologically acceptable interfaces leads to the overall model of the respiratory system. Model uniqueness may be revealed through validation processes and the applicability of two approaches to structural identification and parameter estimation to the models of the respiratory system is demonstrated. A combination of the two techniques (functional minimisation and feature space pattern recognition) in conjunction with sensitivity analysis and model reduction is proposed as a superior means of identification of physiological systems. The comprehensive model of the respiratory system and the subsystem models highlight areas of uncertainty, providing , stimulation for future research in physiological and modelling fields,' Suggestions for further experimentation and theoretical studies in relevant areas are presented.