The computatonal theory and an algorithm are presented which can recover 3D motion parameters and 3D structures of multiple rigidly-moving objects from two-frame feature point correspondences without assuming smoothness of motions nor structures, and without approximating geometry of projection onto the image planes. First, the constraint equation for two-fold transparent 3D motion and structure from correspondences in two perspectively projected frames is derived based on the principle of superposition which is a universal computational principle for multiple motion and motion transparency. Secondly, a quasi-optimal linear algorithm is derived which estimates two-fold multiple motions and structures from noisy correspondence data. The algorithm exploits intermediate constraints as much as possible while keeping its closed-form nature. The algorithm can then cluster the correspondences into two rigid objects in a single-shot manner as well can estimate depths of the correspondence points as a result. It is proved constructively that the solution is unique if the motion and structure is not in special conditions. Finally, a numerical simulation is presented for verifying the proposed algorithm.