Acoustic turbulence has been analyzed in the case where there are two acoustic branches and the key process is the decay of a phonon of one branch into two phonons of another branch in the given case or the emission of a phonon by another phonon through Cerenkov radiation. In addition to the well-known (Kolmogorov) turbulence spectrum and the Rayleigh-Jeans distribution, the kinetic equations were found to have two more power solutions with €_k ~k ~ ¹ and e_k ~k³.