The emerging ability to represent an oscillating moving object over occlusions was studied in 7-21-week-old infants. The object moved at 0.25 Hz and was either occluded at the center of the trajectory (for 0.3 s) or at one turning point (for 0.7 s). Each trial lasted for 20 s. Both eye and head movements were measured. By using two kinds of motion, sinusoidal (varying velocity) and triangular (constant velocity), infants' ability to take velocity change into account when predicting the reappearance of the moving object was tested. Over the age period studied, performance at the central occluder progressed from almost total ignorance of what happened to consistent predictive behavior. From around 12 weeks of age, infants began to form representations of the moving object that persisted over temporary occlusions. At around 5 months of age these representations began to incorporate the dynamics of the represented motion. Strong learning effects were obtained over single trials, but there was no evidence of retention between trials. The individual differences were profound.