This dissertation is an account of how ideas familiar to the engineer were applied to an unusual problem - the modelling of respiratory gas exchange. After a review of the objectives and methods of modelling, a basic model of respiratory gas exchange is developed from simple anatomical and physiological observations. An analogue simulation is developed from this model, and it is shown how this simulation may be linked with standard physiological transducers, and its response compared with that of a normal subject. Several experimental results are given which prove that this simulation gives a good account of CO2 and argon in the expired air of normal resting subjects. A new approximation to the dissociation curves of blood renders the model applicable to oxygen, and appears to explain certain errors found in the modelling of exercising subjects. Two potentially useful cases of the application of modelling are extracted, and are developed in detail. These lead to a possible method for detecting the early onset of respiratory disorders (and possibly for quantifying gross disorders), and for simple measurements of cardiac output, without the usual requirement for blood samples. A model of the chemical control of respiration is then developed in outline, based on the experimental results described above. The basic claim to originality in this work lies not in any novel engineering ideas, but mainly in the new experimental results and the new openings to diagnostic techniques which were obtained. For these results (given in chapters IV - VII) a large degree of originality is claimed. On the other hand, some new sensitivity results in connection with self-adaptive modelling have been brought to light by tackling such an unusual problem. In addition, I hope that the numerate biologist might find this dissertation a useful introductory text to modelling, and the use of obscure words or jargon has been avoided where possible.