A model Bose-Einstein gas is considered in which numerical perturbations in the population of the lowest state have a relaxation time that is long compared with the relaxation time for perturbations in the symmetry of the velocity distribution in the excited states. Oscillations of the population of the lowest state about its equilibrium value are transmitted as second sound waves. The velocity of transmission is found as a function of temperature below the lambda-point and compared with that of second sound in liquid helium. In the gas there is a temperature dependent coupling between pressure waves and thermal waves; the normal modes of propagation are mixed. The high speed mode is pure pressure wave near $T_{\lambda }$ but goes over gradually to pure thermal wave as $T$ goes down towards 0°K; the low speed mode is pure thermal wave near $T_{\lambda }$ but goes over gradually to pure pressure wave as $T$ goes down towards 0°K. For $T\ll T_{\lambda }$ the thermal wave has a higher speed of propagation than the pressure (ordinary sound) wave.

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