  We examine the modular properties of nonrenormalizable superpotential terms
in string theory and show that the requirement of modular invariance
necessitates the nonvanishing of certain Nth order nonrenormalizable terms. In
a class of models (free fermionic formulation) we explicitly verify that the
nontrivial structure imposed by the modular invariance is indeed present.
Alternatively, we argue that after proper field redefinition, nonrenormalizable
terms can be recast as to display their invariance under the modular group. We
also discuss the phenomenological implications of the above observations.
