  It is shown that in SO(10) and SU(5) models having a $U(1)_R$ symmetry, the
requirement of breaking the unified group to the Standard Model leads to flat
directions in the scalar potential. These can lead to a ``cosmological modulus
problem". This is relevant to grand unified models of inflation, where $U(1)_R$
symmetries are often used to insure the flatness of the inflaton potential. A
way that the modulus problem might be avoided is discussed.
