The one‐dimensional initial‐value problem of a monatomic single component gas is considered. Using the linearized Boltzmann equation the dispersion relation is studied. In addition to the usual gas‐dynamic sound waves, one finds an infinity of decaying propagating waves. The phenomenon exhibits itself as a sequence of epochs, the last state of which is hydrodynamic. With reference to the same problem, macroscopic equations such as Euler, Navier‐Stokes, Burnett, moments equations, etc., are considered. In addition, the recently considered ``kinetic models'' of Grosset al.are applied to the problem. These various formulations are critically analyzed and compared with each other and with the Boltzmann analysis. Lastly, several modifications are offered which remedy some of the shortcomings which appear in the approximate theories.