1. The results of non-linear optimization studies on the mechanism of reaction of fully reduced cytochrome oxidase with O2 at 176K are presented. The analysis is carried out on data obtained by means of dual-wavelength multi-channel spectroscopy at three wavelength pairs (604-630, 608-630 and 830-940 nm) and at three O2 concentrations (60, 200 and 1180 micron). The only model that satisfies the triple requirement of a standard deviation within the standard error of the experimental data, good determination of the optimized parameters and a random distribution of residuals is a three-species sequential mechanism. 2. On the basis of the optimized values of the relative absorption coefficients of the intermediates at each wavelength obtained from the present paper together with data from low-temperature trapping, e.p.r. and magnetic-susceptibility studies, the possible valence states of the metal centres in each of the intermediates are discussed.