Given a static string solution with some free constant parameters (''m
oduli'') it may be possible to construct a time-dependent solution by
just replacing the moduli by some functions of time. We present severa
l examples when such a ''rolling moduli'' ansatz is consistent. In par
ticular, the anisotropic D=4 cosmological solution of Nappi and Witten
can be reinterpreted as a time-dependent generalisation of the (analy
tic continuation of the) D=3 ''charged black string'' background with
the ''charge'' changing with time. We find some new D=4 cosmological s
olutions which are ''two rolling moduli'' generalisations of the previ
ously known ones. We also comment on the interplay between duality tra
nsformations and the replacement of moduli by functions of time.