  We study the effect of the antisymmetric tensor field $B_{\mu\nu}$ on the
large curvature phase of string cosmology. It is well-known that a
non-vanishing value of $H=dB$ leads to an anisotropic expansion of the spatial
dimensions. Correspondingly, in the string phase of the model, including
$\alpha '$ corrections, we find anisotropic fixed points of the evolution,
which act as regularizing attractors of the lowest order solutions. The
attraction basin can also include isotropic initial conditions for the scale
factors. We present explicit examples at order $\alpha '$ for different values
of the number of spatial dimensions and for different ans\"{a}tze for $H$.
