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Optical feedback cavity-enhanced absorption spectroscopy (OF-CEAS) has been demonstrated by coupling a distributed feedback diode laser to a ring cavity. Frequency-selected light decaying from the ring cavity is retro-reflected, inducing a counter-propagating intra-cavity beam, and providing optical feedback to the laser. At specific laser-to-cavity distances, all cavity mode frequencies return to the diode laser with the same phase, allowing spectra to be accumulated across the range of frequencies of the current-tuned laser. OF-CEAS has been used to measure very weak oxygen isotopologue ((OO)-O-16-O-18 and (OO)-O-16-O-17) absorptions in ambient air at wavelengths near 762 nm using the electric-dipole forbidden O-2 A-band. A bandwidth reduced minimum detectable absorption coefficient of 2.2x10(-9) cm(-1) Hz(-1/2) is demonstrated.