In string or M theory with a-large compactification radius, some axion
like moduli can be much lighter than the gravitino. Generic moduli in
gauge-mediated supersymmetry breaking models also have a mass;far belo
w the weak scale. Motivated by these, we examine the cosmological impl
ications of light moduli for the mass, range from the weak scale to an
extremely small scale of O(10(-26)) eV, and obtain an upper bound on
the initial moduli misalignment for both cases with and without late e
ntropy production.