Using a variational method, we derive a set of equations of motion for ternary fluids with oil, water, and surfactant. The equations are written in terms of two local concentrations of the components and a local average velocity field. Choosing the free energy functional suitable for microemulsions, we study the dynamics of concentration fluctuations. The time-correlation function of the concentration fluctuations is shown to be generally given by two exponential functions due to the dynamic cross coupling between the two concentration fields. A formula of the stress tensor and the explicit form of the effective diffusion constant arising from the hydrodynamic interaction are also obtained.