We measured thresholds for the monocular discrimination of rigidly and nonrigidly moving objects defined by motion parallax. The retinal projections of rigidly moving objects are subject to certain constraints. By applying smooth 2-D transformations to the projections of rigidly moving objects, we created stimuli in which these constraints were affected. Thresholds for (generic) nonrigid transformations that in theory can be detected from rigid ones by processing pairs of views depended not only on the extent to which the rigidity constraints were affected, but also on the structure and the movement of the simulated object. Nonrigid transformations under which every three successive views had a rigid interpretation were not discriminable from rigid transformations, except in cases where the distortions were very large. Under the rigidity assumption, this would mean that a large class of nonrigidly moving objects is erroneously perceived as rigidly moving.