We studied the horizontal oculomotor neural integrator in healthy human subjects during gaze holding in darkness. We found large variability among subjects with respect to the estimated time constants and the integrator's null position. We also found that individual subjects could demonstrate significantly nonlinear drift velocities as a function of eye position. Nevertheless, a consistent trend did not emerge. Consequently, cross subject averaging eliminates idiosyncratic nonlinear patterns and the average can be approximated by a linear function inside the range that was tested.