The results of acoustooptic measurements of the attenuation coefficient of longitudinal ultrasonic waves in copper halide photochromic glasses are presented for wide temperature (140-550 K) and frequency (190-790 MHz) ranges. In the low-temperature region (T < 230 K), a wide relaxational peak is observed at a frequency of 629 MHz. Presumably, this peak is related to the motion of copper ions in the glass lattice. In the high-temperature region (up to 550 K), the attenuation coefficient does not depend on temperature. The presence of the temperature plateau is explained in the framework of the two-level system model with weak asymmetry.