We investigate whether or not the energy exchange occurs between two species groups of particles in an expanding two-component gravitating system, and we derive the relaxation time scale for energy exchange in such a phase. This is accomplished by solving the dynamic equation coupled with Poisson's equation. We derive a characteristic time determined by the various mass and velocity ratios. When the expansion time does not exceed the characteristic time, energy exchange between the two components is possible and depends on the mass ratio. Once the characteristic time is exceeded, there is virtually no relaxation at all in system. When m2 ≫ m1, the transfer of energy becomes inefficient. Therefore, energy exchange between two species of particle in an expanding two-component gravitating system depends not only on the mass ratio but also on the expansion time.