Glucose oxidase (GO) and copper amine oxidase (CAO) catalyze the reduction of molecular oxygen to hydrogen peroxide. If a closed-shell cofactor (like FADH(2) in GO and topaquinone (TPQ) in CAO) is electron donor in dioxygen reduction, the formation of a closed-shell species (H(2)O(2)) is a spin forbidden process. Both in GO and CAO, formation of a superoxide ion that leads to the creation of a radical pair is experimentally suggested to be the rate-limiting step in the dioxygen reduction process. The present density functional theory (DFT) studies suggest that in GO, the creation of the radical pair induces a spin transition by spin orbit coupling (SOC) in O(2)(-)(rad), whereas in CAO, it is induced by exchange interaction with the paramagnetic metal ion (Cu(II)). In the rate-limiting step, this spin-transition is suggested to transform the O(2)(-)(rad)-FADH(2)(+)(rad) radical pair in GO and the Cu(II)-TPQ (triplet) species in CAO, from a triplet (T) to a singlet (S) state. For CAO, a mechanism for the O[bond]O cleavage step in the biogenesis of TPQ is also suggested.