In recent work Kachru, Kumar, and Silverstein introduced a special class of nonsupersymmetric type II string theories in which the cosmological constant vanishes at the first two orders of perturbation theory. Heuristic arguments suggest the cosmological constant may vanish in these theories to all orders in perturbation theory leading to a flat potential for the dilaton. A slight variant of their model can be described in terms of a dual heterotic theory. The dual theory has a nonzero cosmological constant which is nonperturbative in the coupling of the original type II theory. The dual theory also predicts a mismatch between Bose and Fermi degrees of freedom in the nonperturbative D-brane spectrum of the type II theory. [S0556-2821(98)01724-X].