We present a novel framework for finding the kinematic structure correspondences between two articulated objects in videos via hypergraph matching. In contrast to appearance and graph alignment based matching methods, which have been applied among two similar static images, the proposed method finds correspondences between two dynamic kinematic structures of heterogeneous objects in videos. Thus our method allows matching the structure of objects which have similar topologies or motions, or a combination of the two. Our main contributions are summarised as follows: (i)casting the kinematic structure correspondence problem into a hypergraph matching problem by incorporating multi-order similarities with normalising weights, (ii)introducing a structural topology similarity measure by aggregating topology constrained subgraph isomorphisms, (iii)measuring kinematic correlations between pairwise nodes, and (iv)proposing a combinatorial local motion similarity measure using geodesic distance on the Riemannian manifold. We demonstrate the robustness and accuracy of our method through a number of experiments on synthetic and real data, showing that various other recent and state of the art methods are outperformed. Our method is not limited to a specific application nor sensor, and can be used as building block in applications such as action recognition, human motion retargeting to robots, and articulated object manipulation.