X-band electron paramagnetic resonance on doped Er3+ and Yb3+ ions in Y0.99(Yb,Er)0.01Ba2Cu3OX compounds with different oxygen contents in the wide temperature range (4-120)K have been made. In the superconducting species, the strong dependencies of the linewidth and resonance line position from the sweep direction of the applied magnetic field are revealed at the temperatures significantly below TC. The possible origins of the observed hysteresis are analyzed. Applicability of the presented EPR approach to extract information about the dynamics of the flux-line lattice and critical state parameters (critical current density, magnetic penetration depth, and characteristic spatial scale of the inhomogeneity) is discussed
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