The complex reaction mechanism of tyrosinase involves three enzymatic forms, two overlapping catalytic cycles and a dead-end complex. Analytical expressions for the catalytic and Michaelis constants of tyrosinase towards phenols and oxygen were derived for both, monophenolase and diphenolase activities of the enzyme. Thus, the Michaelis constants of tyrosinase towards the oxygen (K(mO(2))) are related with the respective catalytic constants for monphenols (k(M)(cat)) and o-diphenols (k(D)(cat)), as well as with the rate constant, k(+8). We recently determined the experimental value of the rate constant for the binding of oxygen to deoxytyrosinase (k(+8)) by stopped-flow assays. In this paper, we calculate theoretical values of K(mO(2)) from the experimental values of catalytic constants and k(+8) towards several monophenols and o-diphenols. The reliability and the significance of the values of K(mO(2)) are discussed.