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Light-induced absorption (LIA) characteristics in weakly reduced (or strongly annealed) congruent and/or vapor transport equilibration (VTE)-treated Er-doped LiNbO3 crystals have been investigated in comparison with their corresponding as-grown ones and undoped crystals by using a polarized 632.8-nm beam as probe light and another polarized 632.8- or 488-nm beam as pump light. Under He-Ne pump, the LIA was observed only in strongly reduced pure VTE LiNbO3 crystal. Under 488-nm pump, LIA is still not observed in the doped or undoped as-grown crystals. The weakly reduced VTE-treated Er(0.2 mol?%):LiNbO3 crystal displays weak and stable LIA. On the other hand, the corresponding weakly reduced congruent crystal displays a rather unpredictable light-induced absorption instability phenomenon. The instability was shown by the random competition of the LIA and light-induced transparency (LIT). When both crystals were further reduced, the VTE sample still shows stable LIA but with increased LIA, while the LIA in the congruent sample also becomes stable enough. The instability was experimentally proved to be associated with the presence of the Er3+ ion that performs the role of an extrinsic defect instead of photoluminescence. A three-level model is suggested that consists of a deep level (the bipolaron) and two shallow levels: the small polaron level and the level with respect to the Er3+ ion. The model has been employed to qualitatively explain the LIA characteristics of the weakly reduced congruent Er:LiNbO3 crystal, including the the instability, the effect of the state of reduction, the pump intensity and the pump-probe polarization dependences. The inhomogeneity of the defects caused by the weak reduction and the simultaneous participation of the two shallow levels in the light-induced electron-transport process result in the random competition between LIA and LIT, and consequently result in the LIA instability. [ABSTRACT FROM AUTHOR]