A fiber optic resonant gyroscope in which the laser beam is coupled to a frequency modulator which produces three spatially separated beams frequency shifted from one another by a predetermined amount equal to the difference between the N.sup.th and N.sup.th +1 traveling wire resonant modes of the fiber optic ring, a portion of the outputs from the laser frequency modulator being applied to travel in one direction around the fiber optic ring, a portion of the other two outputs being applied to travel in the opposite direction around the fiber optic ring. Detectors are employed to detect the N.sup.th and, N.sup.th -1 and N.sup.th +1 resonant modes and the signals from these detectors are fed back to the modulators to cause the respective output beams to track the respective modes. The signal values fed back are used to provide an output signal indicative of the Sagnac shift.