A general scheme for the solution of stability problems for two-dimensional flows (the Navier-Stokes equations and shallow water equations) by means of a weakly nonlinear theory is analyzed in the paper. Equations of the first, second and the third order are presented using a perturbation expansion of the stream function of the flow and the method of multiple scales. It is shown that the amplitude evolution equation for the amplitude of the most unstable mode is the complex Ginzburg-Landau equation. The equation is derived using solvability condition at the third order. Possible applications of the Ginzburg-Landau model are discussed in the paper.