  Given a static string solution with some free constant parameters (`moduli')
it may be possible to construct a time-dependent solution by just replacing the
moduli by some functions of time. We present several examples when such
`rolling moduli' ansatz is consistent. In particular, the anisotropic D=4
cosmological solution of Nappi and Witten can be reinterpreted as a
time-dependent generalisation of the (analytic continuation of) D=3 `charged
black string' background with the `charge' changing with time. We find some new
D=4 cosmological solutions which are `two rolling moduli' generalisations of
the previously known ones. We also comment on interplay between duality
transformations and the replacement of moduli by functions of time.
