We introduce a model for the computation of structure-from-motion based on the physiology of visual cortical areas MT and MST. The model assumes that the perception of depth from motion is related to the firing of a subset of MT neurons tuned to both velocity and disparity. The model's MT neurons are connected to each other laterally to form modulatory receptive-field surrounds that are gated by feedback connections from area MST. This allows the building up of a depth map from motion in area MT, even in absence of disparity in the input. Depth maps from motion and from stereo are combined by a weighted average at a final stage. The model's predictions for the interaction between motion and stereo cues agree with previous psychophysical data, both when the cues are consistent with each other or when they are contradictory. In particular, the model shows nonlinearities as a result of early interactions between motion and stereo before their depth maps are averaged. The two cues interact in a way that represents an alternative to the "modified weak fusion" model of depth-cue combination.