NADH:ubiquinone oxidoreductase (complex I) is a complicated respiratory chain enzyme that conserves the energy from NADH oxidation, coupled to ubiquinone reduction, as a proton motive force across the mitochondrial inner membrane. Alternatively, NADH oxidation, by the flavin mononucleotide in complex I, can be coupled to the reduction of hydrophilic electron acceptors, in non-energy-transducing reactions. The reduction of molecular oxygen and hydrophilic quinones leads to the production of reactive oxygen species, the reduction of nicotinamide nucleotides leads to transhydrogenation, and "artificial" electron acceptors are widely used to study the mechanism of NADH oxidation. Here, we use a combined modeling strategy to accurately describe data from three flavin-linked electron acceptors (molecular oxygen, APAD(+), and ferricyanide), in the presence and absence of a competitive inhibitor, ADP-ribose. Our combined ping-pong (or ping-pong-pong) mechanism comprises the Michaelis-Menten equation for the reactions of NADH and APAD(+), simple dissociation constants for nonproductive nucleotide-enzyme complexes (defined for specific flavin oxidation states), and second-order rate constants for the reactions of ferricyanide and oxygen. The NADH-dependent parameters are independent of the identity of the electron acceptor. In contrast, a further flavin-linked acceptor, hexaammineruthenium(III), does not obey ping-pong-pong kinetics, and alternative sites for its reaction are discussed. Our analysis provides kinetic and thermodynamic information about the reactions of the flavin active site in complex I that is relevant to understanding the physiologically relevant mechanisms of NADH oxidation and superoxide formation.