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The behavior of the critical current density of Tl-Ca-Ba-Cu-O superconducting thin films in a cycling magnetic field was investigated. The hysteresis of the transport Jc manifested similar features to those found in polycrystalline Y-Ba-Cu-O and granular Nb, Al thin films in zero-field cooling. However, a novel result of the transport Jc in field-cooled samples has been observed. The results were attributed to the presence of a saturated trapped magnetic flux in the weaklink network. The effects of temperature on both the trapped flux and the transport Jc suggest the existence of various states of the trapped flux in the Tl-based superconducting thin films.