This thesis presents a efficient and robust method for object tracking in compressed video sequences. The method is based on the Optical flow computation algorithm proposed by Hadiashar et al. combined with Fourier filtering, together with a number of other techniques to improve efficiency. Optical flow computation results in motion direction and motion velocity determination at image points. Object motion and contour parameters can be determined from the computed optic flow vectors. The system takes as input an MPEG-1 compressed video sequence and outputs the shape and motion parameters of the moving object. A major feature of the thesis is that it operates on compressed video sequences rather than on uncompressed frames as the traditional object tracking methods do.