  We present a novel Monte Carlo simulation of the phase separation dynamics of
a model fluid membrane. Such a phase segregation induces shape changes of the
membrane and results in local `budding' under favourable conditions. We present
a preliminary investigation of the nucleation regime and compute a variety of
growth laws. Our study indicates that membranes with high viscosity, buckle on
account of phase segregation. We discuss the relation between this dynamical
buckling and the phenomenon of `capping' seen in biological membranes.
