This paper deals with the propagation of the waves (including relaxation, pressure, and density waves) and thermal mode in nonadiabatic and nonequilibrium gases. Based on the mechanism of thermal disturbance feedback, a new governing equation for the propagation of disturbances and the dispersion relation has been obtained. Some new conclusions are reached. For example, the disturbance is either purely growing or slow-damped which presents a reasonable explanation for abnormal absorptive phenomena of infrasonic sound waves in atmosphere; nonadiabatic characteristic of gas can cause a remarkable dispersion phenomena; the propagation of noise can be damped, etc. In addition, the conclusion that pressure and density waves and thermal mode may be unstable agrees with the experimental fact about, thermal instability in high power laser discharges.