The hypothesis that corticocerebellar units projecting to vestibulospinal neurons contribute to the spatiotemporal response characteristics of forelimb extensors to animal displacement was tested in decerebrate cats in which the activity of Purkinje cells and unidentified cells located in the cerebellar anterior vermis was recorded during wobble of the whole animal. This stimulus imposed to the animal a tilt of fixed amplitude (5 degrees) with a direction moving at a constant angular velocity (56.2 degrees/s), both in the clockwise and counterclockwise directions over the horizontal plane. Eighty-three percent (143/173) of Purkinje cells and 81% (42/52) of unidentified cells responded to clockwise and/or counterclockwise rotations. In particular, 116/143 Purkinje cells (81%) and 32/42 unidentified cells (76%) responded to both clockwise and counterclockwise rotations (bidirectional units), while 27/143 Purkinje cells (19%) and 10/42 unidentified cells (24%) responded to wobble in one direction only (unidirectional units). For the bidirectional units, the direction of maximum sensitivity to tilt (Smax) was identified. Among these units, 24% of the Purkinje cells and 26% of the unidentified cells displayed an equal amplitude of modulation during clockwise and counterclockwise rotations, indicating a cosine-tuned behavior. For this unit type, the temporal phase of the response to a given direction of tilt should remain constant, while the sensitivity would be maximal along the Smax direction, declining with the cosine of the angle between Smax and the tilt direction. The remaining bidirectional units, i.e. 57% of the Purkinje cells and 50% of the unidentified cells displayed unequal amplitudes of modulation during clockwise and counterclockwise rotations. For these neurons, a non-zero sensitivity along the null direction is expected, with a response phase varying as a function of stimulus direction. As to the unidirectional units, their responses to wobble in one direction predict equal sensitivities along any tilt direction in the horizontal plane and a response phase that changes linearly with the stimulus direction. By comparing these data with those obtained previously during selective stimulation of macular receptors by a 5 degrees off-vertical axis rotation, it appeared that the directions of maximum sensitivity to tilt were distributed over the whole horizontal plane of stimulation, in both conditions. However, co-stimulation of macular and canal receptors during wobble decreased the proportion of unidirectional units, while that of the bidirectional, namely broadly tuned units, increased. In addition, while the average gain of the Smax vector of the bidirectional units was comparable, the temporal phase of this vector tended to show a more prominent phase leading behavior during wobble with respect to off-vertical axis rotation. The possibility that the tested neurons formed a population which coded the direction of head tilt in space was also investigated using a modified version of the classical population vector analysis. It was shown that for each selected time in the tilt cycle the direction of the population vector closely corresponded to that of the head tilt, while its amplitude was related to that of the stimulus. We conclude that the broad distribution of the response vector orientation of units located in the cerebellar anterior vermis represents an appropriate substrate for the cerebellar control of vestibulospinal reflexes involving extensor muscles during a variety of head tilts. In view of their efferent projections to the vestibular and fastigial nuclei, the cerebellar anterior vermis may provide a framework for the spatial coding of vestibular inputs, giving equal emphasis to both side-to-side and fore-aft stability.