On the basis of a theoretical analysis and numerical calculations, it has been shown that the dynamics of a flame surface under conditions of hydrodynamic instability can be represented as the interaction of a finite number of nonlinear configurations of the flame front. Their number is defined by the physical size of the system in which the flame propagates. It has been shown that the development of an initial plane front leads to a stationary regime at which the propagation velocity of the curved flame tends asymptotically to its limiting value independent of the size of the system in which burning takes place. This conclusion is based on the exact solution of the nonlinear equation describing hydrodynamic instability of flame.