Oscillation conditions were determined for acoustically distributed feedback (ADFB) lasers based on gyrotropic uniaxial and cubic crystals. The lasing threshold was shown to be higher for the modes with clockwise polarization than for those with counterclockwise polarization. It is established that the regions of maximal amplification for clockwise (counterwise) waves of the gyrotropic crystal are displaced in the direction of decreased (increased) phase detuning, respectively, relative to amplification regions that correspond to the absence of crystal gyrotropy. The ADFB laser was shown to be capable of generating at the Bragg frequency.