In this paper, we describe a new approach to the continuous operation of a transverse spin-exchange optically pumped NMR gyroscope that utilizes modulation of both the applied bias field and the optical pumping. We demonstrate the simultaneous, continuous excitation of131Xe and129Xe using this hybrid modulation approach and the real-time demodulation of the Xe precession using a custom least-squares fitting algorithm. We present rotation rate measurements with this device, with a common field suppression factor of ∼1400, an angle random walk of 21μHz/Hz, and a bias instability of ∼480 nHz after ∼1000 s.