Abstract: In this thesis, I describe three approaches to the continuous operation of a transverse spin-exchange optically pumped NMR gyroscope. I demonstrate the simultaneous, continuous excitation of $^{131}$Xe and $^{129}$Xe using first modulations of the optical pumping (polarization modulation, PM), then using modulations of the applied bias field (pulse density modulation, PDM), and then using a combined approach that includes both polarization and field modulations (hybrid operation). I describe the theory behind the operation of the device, and the apparatus used to perform the experiments presented in this thesis. I then present results for each of the three operation modes - PM, PDM, and hybrid operation. For each, I give several key performance metrics, including linewidth, signal-to-noise ratio, field suppression factor, cross talk, angle-random walk, and bias instability. The field suppression factor and cross talk are unique metrics which have generally been ignored in this field of study. This thesis includes the best bias instability ever measured with this device, at $\sim$420~nHz. I close with a comparison of the three methods and a discussion of proposed future works.