Luminescent properties of alexandrite crystals (BeAl2O4:Cr3+) are studied. Partial readouts of thermoluminescence (TL) and optically stimulated luminescence (OSL) signals were obtained to infer the relations of OSL and TL trapping centers. Four TL peaks were studied; their intensities decrease at different rates by illumination with blue OSL light. The OSL curve shows two-time components (exponential decay constants 3.15 and 28.4 s). The short time component is preferentially diminished when the sample is heated to temperatures from 363 to 513 K. About 50% of the whole TL intensity remains after a complete 300s OSL readout.