Target space duality (T duality), which interchanges Kaluza--Klein and
winding-mode excitations of the compactified heterotic string, is realized as a
symmetry of a world-sheet action. Axion-dilaton duality (S duality), a
conjectured nonperturbative SL(2,Z) symmetry of the same theory, plays an
analogous role for five-branes. We describe a soliton spectrum possessing both
duality symmetries and argue that the theory has an infinite number of dual
string descriptions.Comment: 16 pages, NSF-ITP-93-6