Nuclear spin-lattice relaxations ofBe9andAl27in an alexandrite(BeAl2−xCrxO4,x=0.02) single crystal have been investigated in the temperature range 140 K–400 K. The paramagnetic impurity effect on the relaxation is negligible for both nuclei. The relaxation of theBe9nuclear spins is found single exponential in time when the whole resonance lines are uniformly excited. When only the central resonance line is excited forAl27, the relaxation is well fitted with a linear combination of three exponential functions given by Simmons &etal; [Phys. Rev.127, 1168 (1962)]. Since the spin-lattice relaxation rate is proportional to the square of temperature for both nuclei, the dominant relaxation mechanism in this temperature range can be inferred as the Raman process. ©1997 American Institute of Physics.