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Magnetic reconnection is a fundamental process in astrophysical, space and laboratory plasma. In essence, it represents reorganization of topology of the magnetic field caused by a change of structure of its power lines. This change leads to release of a saved-up magnetic energy. In work process of transformation of structurally unstable magnetic configurations in the structurally steady is considered from the point of view of the theory of catastrohy. The special attention is paid to modeling of evolution of structurally unstable three-dimensional magnetic fields.