<正> Ⅰ. INTRODUCTIONAlexandrite is a hopeful laser crystal not only because the sharp R-line shows laser action, as in ruby, but also the vibronic sideband is involved in the lasing of this crystal, in this case the system is of four-levels and is widely tunable (700 nm--800 nm). We have studied the dynamic properties of the excited states of Cr3+ in BeAl2O4. The relaxation of the system within the excited states reveals the dynamics of the interactions of the ion defects with phonons. As the time of relaxation is