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We present an interactive algorithm to perform continuous collision detection between general deformable models using graphics processors (GPUs). We model the motion of each object in the environment as a continuous path and check for collisions along the paths. Our algorithm precomputes the chromatic decomposition for each object and uses visibility queries on GPUs to quickly compute potentially colliding sets of primitives. We introduce a primitive classification technique to perform efficient continuous self-collision. We have implemented our algorithm on a 3.0GHz Pentium IV PC with a NVIDIA 7800GPU, and we highlight its performance on complex simulations composed of several thousands of triangles. In practice, our algorithm is able to detect all contacts, including self-collisions, at image-space precision in tens of milli-seconds.