In this chapter, we investigate the dynamics of heterogeneity observed in multicomponent fluid membranes, particularly focusing on hydrodynamic effects due to the membrane and solvent. Two situations are discussed separately: above and below the miscibility transition temperature. In the former case, we calculate the wave number dependence of the effective diffusion coefficient by changing the temperature and/or the thickness of the bulk fluid. We also obtain the effective diffusion coefficient when multicomponent membranes are regarded as two-dimensional microemulsions. For the case below the transition temperature, we study the domain growth exponent in a binary membrane using a particle-based simulation method. With the addition of bulk solvent, a change in the growth exponent from two- to three-dimensional nature is observed. Along with the measurement of correlated diffusion, we conclude that the phase separation takes place through the Brownian coagulation process in our simulation. We shall review some other works which are related to the present subject.