The dynamic behaviour of the modified Pople-Karasz model is studied by the direct relaxation method and the path probability method. First the equilibrium behaviour of the model is given briefly in order to understand the dynamic behaviour. Then the direct relaxation method, which is based on the detailed balance conditions, and the path probability method are applied to the model and the dynamic equations or the rate equations are obtained. Dynamic equations are solved either by means of the flow diagram or by using the Runge-Kutta method, or both. The stable, metastable and unstable solutions are shown in the flow diagrams explicitly, and the role of the unstable state as separators between the stable and metastable is described. Moreover, the "flatness" property of the metastable state and the "overshooting" phenomenon are seen explicitly from the relaxation curves of the order parameters. (C) 2003 Elsevier Science B.V. All rights reserved.