Abstract: Although deforming surfaces are frequently used in numerous domains (scientific applications, games...), only few works have been proposed until now for simplifying such data. However, these time-varying surfaces are generally represented as oversampled triangular meshes with a static connectivity, involving a large number of unnecessary details for some frames. Among the related works, some methods provide good results, but fine details appearing during the animation are not always well-preserved, because of a static geometry sampling. So, we propose a new simplification method for deforming surfaces based on a dynamic geometry sampling. The idea is to compute one coarse version at the first frame, and then to progressively update the coarse sampling for the subsequent frames. In order to optimally approximate each frame, vertices are added or removed following the appearance or disappearance of fine details in the frames. Our approach is fast, easy to implement, and produces good quality time-varying approximations with well-preserved details, at any given frame.