The evolution of components of close binary systems of intermediate mass (component masses in the range 3--12 M/sub sun/) and of Population I composition (X = 0.7, Z = 0.02) is studied numerically. We assume that a model star first fills its Roche lobe after it has developed a helium core and becomes a giant and that mass loss from the model continues until model radius decreases below a predetermined limit. How much of the matter that is lost from the Roche-lobe--filling model is transferred to its companion and how much is lost from the system are left undetermined. In the mass loss/exchange process, a model of initial mass in the 3--10 M/sub sun/ range is transformed into a compact ''helium'' star (which, nevertheless, retains some hydrogen-rich matter in its envelope). In our experiments, models of initial mass 3, 4, 5 6.95, and 9.85 M/sub sun/ produce remnants of mass 0.378, 0.523, 0.765, 1.11, and 1.95 M/sub sun/, respectively. The lifetime of the core helium-burning phase of each remnant ranges from 200% (.0378 M/sub sun/ remnant) to 20% (1.95 M/sub sun/ remnant) of the main-sequence lifetime of its progenitor, and the possibility arises that the primordial secondary, if it ismore » initially massive enough or if it has accreted sufficient matter during the first mass-transfer episode, will expand and transfer matter back to the primary remnant while this remnant is still relatively compact. We show that, then, most of the matter outside the helium core of the secondary will be ejected from the system.« less