We present a new approach for motion estimation from digital videos based on the use of 2D amplitude-modulation frequency-modulation (AM-FM) models. The proposed approach uses an AM-FM representation to derive AM and FM based equations that can be applied to two consecutive frames to derive motion estimates. We test the proposed method using complex synthetic examples, with both amplitude-modulated and frequency-modulated components, for both sinusoidal, periodic motions and constant motion and compare against the popular Horn-Schunk and Lucas and Kanade method. Compared to the standard Horn-Schunk and Lucas and Kanade methods, the proposed approach leads to dramatic reductions in the mean-squared error for both constant, translational motion (from 19.73% to 95.46% reduction) and complex sinusoidal, periodic motions (up to 67.95% reduction).