When viewing an event in which an object moves behind an occluder on part of its trajectory, 4-month-old infants perceive the trajectory as continuous only when time or distance out of sight is short. Little is known, however, about the conditions under which young infants perceive trajectories to be discontinuous. In the present studies we focus first on infants’ perception of trajectories that change during a period of occlusion. Four-month-olds perceive discontinuity in trajectories that change in height or orientation while behind an occluder, and this is true even when a change in direction could be due to an invisible bouncing collision with a surface. Further experiments reveal that infants do not perceive diagonal linear trajectories as continuous across an occlusion unless the occluding and revealing edges are orthogonal to the path of movement. Implications for theories of perceptual and cognitive development are discussed.