We use analytic models to compute the evolution of the core of a stellar system due simultaneously to stellar evaporation which causes the system (core) to contract and to its binaries which cause it to expand by progressively decreasing its binding energy. The evolution of the system is determined by two parameters: the initial number of stars in the system N$sub 0$, and the fraction f/subb/ of its stars which are binaries. For a fixed f/subb/, stellar evaporation initially dominates the dynamical evolution if N$sub 0$ is sufficiently large due to the fact that the rate of evaporation is determined chiefly by long-range encounters which increase in importance as the number of stars in the system increases. If stellar evaporation initially dominates, the system first contracts, but as N/subc/, the number of remaining stars in the system, decreases by evaporation, the system reaches a minimum radius and a maximum density and then it expands monotonically as N/subc/ decreases further. Open clusters expand monotonically from the beginning if they have anything approaching average Population I binary frequencies. Globular clusters are highly deficient in binaries in order to have formed and retained the high- density stellar cores observed in most of them.more » We estimate that for these system f/subb/ < or = 0.15. (AIP)« less