An entire class of non-isotropic generalizations of the FRW string bac
kgrounds is presented, essentially supplying the string-cosmology coun
terpart of the diagonal Bianchi-type models in general relativity. Lea
ding-order solutions with vanishing cosmological constant and time-dep
ended axion/dilaton scalars have been found for all types. They includ
e as special cases all hitherto known solutions within this class, whi
le the limits of SO(3) isotropy supply all possible FRW backgrounds. T
here is always an initial singularity and no inflation. Other features
of the solutions which can illuminate the impact of spatial anisotrop
ies on the dynamics of the early universe, as well as their behaviour
under abelian T-duality, are discussed.