The kinetic behaviour of chicken-liver xanthine dehydrogenase (xanthine/NAD+ oxidoreductase; EC 1.2.1.37) has been studied. Steady-state results, obtained from a wide range of concentrations of substrates and products, were fitted by rational functions of degree 1:1, 1:2, 2:2 and 3:3 with respect to substrates, and 0:1, 1:1, 0:2 and 1:2 with regard to products, using a non-linear regression program which guarantees the fit. The goodness of fit was improved using a computer program that combines model discrimination, parameter refinement and sequential experimental design. The AIC and F tests were also used for model discrimination. For comparative purposes, the xanthine/oxygen oxidoreductase reaction was also studied. From the functions which give the maximum improvement, the complete rate equation was deduced. The significance of the terms was stated by the above methods. It was concluded that xanthine dehydrogenase requires a minimum mechanism of degree 1:1 for xanthine, 2:2 for NAD+, 1:1 for uric acid and 1:2 for NADH in the xanthine/NAD+ oxidoreductase reaction. These are the minimum degrees required but a rate equation of higher degree is not excluded.