Thresholds for the detection of motion in depth in the median plane of the head are substantially poorer than those for motion in the frontoparallel plane. This suggests the existence of two independent mechanisms for their detection. Any three-dimensional (3-D) motion can be decomposed into components of motion in the frontoparallel plane and in the median plane of the head. Can human performance for the detection and discrimination of other 3-D motions be predicted by a combination of responses from the two independent mechanisms? Minimum displacement thresholds (d(min)) for the detection of 3-D motion and the direction discrimination of 3-D motion were measured for a wide range of 3-D directions. d(min) data were modelled in terms of the probability summation of a pair of independent motion mechanisms, one responding to motion in the median plane of the head, the second to motion in the frontoparallel plane. Detection of 3-D motion was well predicted by probability summation across a range of 3-D directions. Direction discrimination of 3-D motion was similarly well fit by the probability summation model for multiframe motion displays for some observers. However for two-frame motion displays, direction discrimination for 3-D motion was best fit by a model using only a motion mechanism in the frontoparallel plane. Detection and direction discrimination thresholds for 3-D motion can therefore be explained on the basis of one or two mechanisms, sensitive to motion in the frontoparallel plane and in the median plane of the head.