We consider how tracking in stereo may be enhanced by coupling pairs of active contours in different views via affine epipolar geometry and various subsets of planar affine transformations, as well as by implementing temporal constraints imposed by curve rigidity. 3D curve tracking is achieved using a submanifold model, where it is shown how the coupling mechanisms can be decomposed to cater for fixed and variable epipolar geometries. In the case of tracking planar curves, the canonical frame model is developed such that the various geometrical constraints needed in different situationsmay be efficiently selected. The results show that coupled active contours add consistency and robustness to tracking in stereo.