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The concentration and pressure dependent luminescence properties of the Tb3+ ions in a lithium fluoroborate glasses have been studied by analyzing the deexcitation processes of the 5D4 level at ambient conditions as well as a function of pressure up to 35 GPa at room temperature. The luminescence spectra of Tb3+ ions have been measured as a function of pressure and observed a continuous redshift as well as a progressive increase in the magnitude of the crystal-field splittings for the 5D4→7F3,4,5 transitions. Monitoring the 5D4→7F5 transition, the luminescence decay curves have been measured and analyzed in order to understand the dynamics of the deexcitation of the Tb3+ ions in these glasses. At ambient conditions a nonexponential behavior has been found for doping concentrations as low as 0.1 mol % of Tb4O7, although no cross-relaxation channels exist to explain this behavior. The modelization of the energy transfer processes surprisingly shows that the nonexponential character of the decay curves of the 5D4 level with concentration or with pressure has to be ascribed to energy transfer to traps without migration of energy between Tb3+ ions. For all the experimental situations the nonexponential character of the decay curves is well described by the generalized Yokota&-Tanimoto model with a dipole-dipole interaction between the Tb3+ ions and the nearby luminescence quenching traps. The luminescence properties observed with releasing pressure are slightly different to those obtained while increasing pressure suggesting a local structural hysteresis in the lithium fluoroborate glass matrix giving rise to the generation of a new distribution of environments for the Tb3+ ions.