Vortex-induced magnetic reconnection (VIMR) and bursty single X line reconnection (BSXR) at the magnetopause are studied using two-dimensional MHD simulation. The VIMR and BSXR occur when the flow-aligned Alfv¿n Mach number is greater or less, respectively, than a critical value which typically ranges from 0.3 to 0.6 for different anomalous resistance conditions. In the former case, the streamlines and magnetic field lines are in alignment and construct a concentric vortical pattern, whereas in the latter case, magnetic field lines do not form closed loops, and vortices occur around the X line. The topological structure of the asymptotic quasi-steady state of 2-D reconnection depends strongly upon the topological invariants such as the cross helicity. The different sites where VIMR and BSXR work at the magnetopause to form flux transfer events are discussed. ¿ American Geophysical Union 1995