In this paper we apply a new data driven 3D prediction step for active contour models to car tracking on highways. The so called 3D bounding volume (BV) is a coarse 3D representation of a moving object, for which the 2D contour in the image plane has been extracted and tracked by active contours. By calculating the BV's shape and location in 3D an estimation of the object's motion is possible. Thus, in contrast to pure 2D tracking of the object's contour by active contour models knowledge about 3D motion is available. This is necessary, if changes in the object's contour - for example, due to rotation - needs to be predicted. We present experiments in the area of car tracking, which show that tracking the cars by active contour models can be improved by the proposed 3D prediction step. In addition, relative statements about the direction of the motion and the velocity of the cars are possible.