Current views on the nature of the haemoglobin-oxygen equilibria have been reviewed and the need for improved experimental techniques stated. A multiple-addition mixing technique for investigation of the equilibria, together with the neccessary ancillary techniques, has been developed and an exhaustive mathematical analysis of the results, using a specially written computer programme, described. A detailed validation of the techniques has been carried out and their particular advantages and disadvantages compared with other techniques. The multiple-addition mixing technique has been used to investigate the effects of pH on the parameters of some of the more important models for the haemoglobin- oxygen equilibria and the results compared with those predicted from theoretical considerations. None of the models considered emerged as a complete description of the data obtained and guidelines for the development of new models have been given.