We propose an extension of parametric active contours designed to track nonoccluding objects transiently touching each other, a task where both parametric and single level set-based methods usually fail. Our technique minimizes a cost functional that depends on all contours simultaneously and includes a penalty for contour overlaps. This scheme allows us to take advantage of known constraints on object topology, namely, that objects cannot merge. The coupled contours preserve the identity of previously isolated objects during and after a contact event, thus allowing segmentation and tracking to proceed as desired.