Abstract: The unsteady two-dimensional equations of the hydrodynamics of the self-gravitational gaseous model have been calculated, using the local solutions of linear density waves as the initial conditions. The results show that there exists rapid nonlinear growth of galactic density waves and the peak value of the flucuating surface density is equivalent to the basic surface density, during the interval of about 5×10⁷ years. The evolutional processes of the waves clearly exhibit nonlinear characteristics.