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The effect of the magnetic flux creep on the levitation stability of high-temperature superconductors was studied. It was shown experimentally that under a unipolar magnetization the levitation force decreased at a logarithmic velocity characteristic of the creep process. If the current structure was bi- or multi-polar one, which was formed in a sample exposed to a reversing external magnetic field, the force remained unchanged during a certain period of time. The theory of relaxation of magnetization and force for a partial and full penetration of the critical state was considered. It was shown that relaxation decelerated sharply if the region with a current producing the main magnetization was far from the superconductor surface. A concept of an open and internal magnetic relaxation was introduced. The time of the internal relaxation for different reverse depths was estimated. The calculated values approached the experimental values of the levitation stabilization time. © 2002 Elsevier Science Ltd. All rights reserved.