1. Rotation about an off-vertical axis (OVAR) causes continuous unidirectional nystagmus in darkness. An analysis of the dynamics of the nystagmus suggests that the continuous slow-phase velocity is generated by a signal that is an estimate of the velocity of a traveling wave pattern associated with the excitation and inhibition of the cells of the otolith maculae. The estimated velocity signal then excites the velocity storage integrator. 2. A mathematical model has been developed that shows how the velocity of the traveling wave might be estimated from patterns of otolith activation related to head position. The estimation of velocity is based on a "template matching" algorithm. It is assumed that the signal arising in each cell of the macula is delayed by a certain time (T). As the head rotates in the gravitational field, a delayed pattern representing a previous position of the head is available as a "template" that can be compared to the pattern associated with the present position of the head. 3. The delayed signal level for each cell is approximated from the present pattern by a spatial extrapolation in pattern space using information from the given cell and an adjacent one. The value of the displacement that minimizes the mean square error between the extrapolated and the delayed signal values over all cells gives a best estimate of head rotation (d) in time T. The estimated head velocity is proportional to the estimated head displacement (d) and inversely proportional to the delay time (T). 4. By using a linear spatial extrapolation function and assuming a uniformly spaced distribution of polarization vectors over 360 degrees, sinusoidal spatial patterns are obtained. The formula for the estimated head velocity (ŵ) reduces to a sinusoidal function of angular head velocity (w) and delay time (T). For T = 0.85 seconds, the model predicts that the steady state estimate of head velocity will rise as a function of stimulus velocity (w) to a peak value at w = 50 deg/sec. The estimate then declines for larger values of stimulus velocity (w). This type of behavior is observed in the slow-phase velocity characteristics of OVAR in monkeys. 5. The model predicts that when animals are tilted after prolonged rotation about a vertical axis, the estimate of head velocity is delayed relative to actual head velocity. This accounts for the delay in the buildup of slow-phase velocity during the initial second.(ABSTRACT TRUNCATED AT 400 WORDS)