A description is given of a curvature-based approach to motion analysis of nonrigid surfaces. Based on changes in the mean and Gaussian curvatures during the motion, it is possible to classify the motion of a surface at each point as rigid, isometric, homothetic, conformal, and general (nonconformal). The general theory of curvature changes for all types of motions is presented. Then the formula specifying changes in the Gaussian curvature during homothetic motion is derived. Also, two special cases of nonrigid motion are considered. The first case deals with piecewise rigid motion. An algorithm is presented which separates a piecewise rigid surface into its rigid parts. The second case deals with homothetic motion. A method is given to isolate regions of the surface where the homothetic assumption is violated. Both algorithms are tested on simulated data and results.