In this communication we present results of measurements of low temperature thermoluminescence, isothermal decays, steady state radioluminescence yield, and scintillation time profiles at various temperatures on two scintillator materials, BaF2:Ce and undoped BaF2. We find that all these results can be consistently interpreted in the frame of a model that includes several relatively shallow charge traps. We have identified and characterized one particular shallow trap that causes the decay of the dominant scintillation component of BaF2 :Ce to be slower than radiative, as well as a set of others that are responsible for even slower components in the scintillation time profile of this material.PACS numbers: 78.60. Kn, 78.60.Ya, 78.55.Hx, 29.40.Mc Thermoluminescence provides a useful tool for studying host-to-ion energy transfer and the role of traps in scintillator materials. While it is generally accepted that deep traps, revealed by high-temperature thermoluminescence (htTL, 300 K and higher) can reduce the scintillation light yield of any scintillator material [1,2], the importance of shallower traps has only recently been recognized [3][4][5]. Although their glow peaks fall at temperatures well below ambient, such shallower traps can introduce slow components in both the rising and decaying parts of the scintillation time profiles and reduce the scintillation light yield at room temperature (RT). Specific examples of these effects have recently been identified in LuAP:Ce (LuAlO3:Ce) and YAP:Ce (YAlO3:Ce) [4,5]. In this communication we report results of studies on BaF2:Ce, a promising scintillator material [6] as well