The dynamical evolution of two-component star clusters, each of which is enclosed within a perfectly reflecting sphere, is investigated by numerically solving moment equations derived from the Boltzmann equation. One of the two adopted model clusters evolves, starting from a state of no mass segregation, toward an equilibrium state at a quite slow rate. The other one evolves away from an equilibrium state and its central density increases without limit. The different evolutionary behaviors of the two model clusters are explained by the fact that there exists no equilibrium state for such clusters if the total energy is less than a certain critical value. The critical value increases with increasing total mass fraction of the heavier stars. This is qualitatively the same as Spitzer's theorem (1969) expressed in another way.