This paper presents several algorithms for estimating motion and structure parameters from long monocular image sequences by using the most apporpriate of a set of long sequence motion models. We first present a new two-view motion algorithm and then extend it to long sequence motion analysis. The two-view motion algorithm generally requires six pairs of point correspondences to give a unique solution of the motion parameters. However, when the points used for correspondences lie on a Maybank Quadric, the algorithm requires seven pairs of point correspondences to give all possible double solutions. Object-centred motion representations and models of motion described by up to the second order polynomials are analysed. Two long sequence algorithms arc presented, one using inter-frame matches, and the other using point trajectories. The long sequence algorithms automatically find the proper model that applies to an image sequence and gives the globally optimal solution for the motion and structure parameters under the chosen model. Experimental results with several real image sequences undergoing different motions are presented to demonstrate the performance of the algorithm.