In the current study, the dynamic evolution of two-phase vesicles is presented as an extension to a previous stationary model and based on equilibrium of local forces. In the simplified model, ignoring the effects of membrane inertia, a dynamic equilibrium between the membrane bending potential and local fluid friction is considered in each phase. The equilibrium equations at the domain borders are completed by extended introduction of membrane section reactions. We show that in some cases the results of stationary and evolutionary models are in compliance with each other and also with experimental observations, while in others the two models differ markedly. The value of our approach is that we can account for unresponsive vague points using our equations with the local velocity of the lipid membranes and calculating the intermediate states (shapes) in the path of evolution. Furthermore the effect of nonhomogeneous distribution of spontaneous curvature on shape transformation of two-phase vesicles is studied via an evolutionary method. The variation of spontaneous curvature is assumed to be a function of arc length in each domain considering the effects of inducing factors (surrounding solution concentration and the membrane-protein interactions such as scaffolding and insertion). Membrane pearling from a large vesicle is simulated by the model and compared with the result of constant curvature and also with empirical observations. It can be shown that accurate simulation of some membrane deformation mechanisms depends on careful consideration of key factors such as the SC variations. In addition, the importance of different uniform and non-uniform distributions of spontaneous curvature is discussed with reference to specific cases. Keywords : Two-phase vesicle , Evolutionary model, Membrane elastic force, Friction force, Variable spontaneous curvature, Protein distribution