  In string/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 below the weak scale.
Motivated by these, we examine the cosmological implications of light moduli
for the mass range from the weak scale to an extremely small scale of order
10^{-26} eV, and obtain an upper bound on the initial moduli misalignment for
both cases with and without a late entropy production.
