The transient-state kinetics of enzyme systems far from equilibrium have been analyzed by a theoretical treatment of the generalized King-Altman mechanism for enzyme reactions. Conditions are defined under which the kinetics differential equations for this generalized mechanism can be analytically solved, and the structure of the analytical solution is characterized. The practical implications of the theoretical results are discussed with reference to the planning, evaluation, and interpretation of transient-state kinetic experiments performed by stopped-flow techniques.