Visual-movement sensitivity of neurons in the turtle's accessory optic system was investigated. Neuronal responses to stimulus direction and speed were analyzed to determine whether they reflect processing by a one-dimensional encoder of visual motion or whether they indicate directional integration of presynaptic direction-sensitive responses whose maximal-response directions are distributed. Both of these mechanisms make predictions about the functional relationship between stimulus direction and response. The responses of single units in the basal optic nucleus to visual stimulation in different directions were described by both cosine and wrapped normal fitting functions. The wrapped normal function (a Gaussian curve mapped onto a circle) performed at least as well as the cosine function and described directional tuning curves of varying widths. Unlike cosines, the addition of two wrapped normals could describe multi-lobed directional data. Next, it was demonstrated that these neurons did not encode visual motion projected onto a single, spatial axis. Responses to the projected speed along the maximal-response direction were systematically lower than responses to the actual speed along that direction. Thus, for speeds above 1°/s, neuronal response varies with respect to direction but not speed. Summation of presynaptic direction-sensitive responses with distributed maximal-response directions (referred to as directional integration) is discussed as a means of accounting for these results.