We present a novel algorithm to perform continuous collision detection(CCD) between non-rigid, deformable models using local advancement. Given the initial and final configurations of a deformable model, our algorithm computes linear deformation by interpolating the vertices from the initial to the final configurations with a straight line path and checks for collision along that path. Our approach is applicable to polygon-soup models with arbitrary topology, handles self-collisions and makes no assumption about the underlying non-rigid motion. We accelerate the algorithm by computing motion bounds on the primitives and their bounding volumes. These bounds are combined with hierarchical culling techniques and used for fast collision checking. In practice, we have observed up to four times improvement in running time because of local advancement.