The mechanism by which cyclooxygenase-1 (COX-1), a heme- and tyrosyl radical-containing enzyme, catalyzes the regio- and stereospecific oxygenation of polyunsaturated fatty acids to prostaglandin or hydroperoxide products has not been understood. Steady-state kinetic studies conducted with the native substrate arachidonic acid and the slower substrate linoleic acid are described here. Second-order rate constants, kcat/KM for fatty acid and O2, are found to depend upon the concentration of the other cosubstrate. Competitive oxygen kinetic isotope effects (18O KIEs) kcat/KM(16,16O2)/kcat/KM(18,16O2) reveal that a peroxyl radical is formed in or before the first kinetically irreversible step. Together, the results indicate that the oxygenase reaction occurs by a sequential mechanism which most likely involves reversible abstraction of a hydrogen atom from the fatty acid prior to the trapping of the delocalized substrate radical by O2. The identity of the first kinetically irreversible step, subsequent to forming the peroxyl radical, is also discussed in the context of the magnitude of the oxygen kinetic isotope effects as well as the behavior of kcat/KM(O2) in response to changing solvent pH, pD, and viscosity.