In this article, the propagation of generalized thermoelastic plane harmonic waves in homogeneous anisotropic media has been investigated. Four types of waves, namely a quasilongitudinal, two quasitransverse, and a thermal wave, are found to exist. The thermal mode, which was diffusive in nature in the nonthermal relaxation case, now becomes wavelike with a finite, though large, wave speed. The results obtained theoretically have been verified numerically and are represented graphically for a single crystal of magnesium.