The perception of the unity of objects, their permanence when out of sight, and the ability to perceive continuous object trajectories even during occlusion belong to the first and most important capacities that infants have to acquire. Despite much research a unified model of the development of these abilities is still missing. Here we make an attempt to provide such a unified model. We present a recurrent artificial neural network that learns to predict the motion of stimuli occluding each other and that develops representations of occluded object parts. It represents completely occluded, moving objects for several time steps and successfully predicts their reappearance after occlusion. This framework allows us to account for a broad range of experimental data. Specifically, the model explains how the perception of object unity develops, the role of the width of the occluders, and it also accounts for differences between data for moving and stationary stimuli. We demonstrate that these abilities can be acquired by learning to predict the sensory input. The model makes specific predictions and provides a unifying framework that has the potential to be extended to other visual event categories.