  We give the general analytic solutions derived from the low energy string
effective action for four dimensional Friedmann-Robertson-Walker models with
dilaton and antisymmetric tensor field, considering both long and short
wavelength modes of the $H$-field. The presence of a homogeneous $H$-field
significantly modifies the evolution of the scale factor and dilaton. In
particular it places a lower bound on the allowed value of the dilaton. The
scale factor also has a lower bound but our solutions remain singular as they
all contain regions where the spacetime curvature diverges signalling a
breakdown in the validity of the effective action. We extend our results to the
simplest Bianchi I metric in higher dimensions with only two scale factors. We
again give the general analytic solutions for long and short wavelength modes
for the $H$ field restricted to the three dimensional space, which produces an
anisotropic expansion. In the case of $H$ field radiation (wavelengths within
the Hubble length) we obtain the usual four dimensional radiation dominated FRW
model as the unique late time attractor.
