  The S-duality invariance of the equations of motion of four dimensional
string effective action with cosmological constant, $\Lambda $, is studied. It
is demonstrated that the S-duality symmetry of the field equations are broken
for nonzero $\Lambda$. The ``naturalness'' hypothesis is invoked to argue that
$\Lambda $ should remain small since exact S-duality symmetry will force the
cosmological constant to vanish in the string effective action.
