  Non-singular Bianchi type I solutions are found from the effective action
with a superstring-motivated Gauss-Bonnet term. These anisotropic non-singular
solutions evolve from the asymptotic Minkowski region, subsequently
super-inflate, and then smoothly continue either to Kasner-type (expanding in
two directions and shrinking in one direction) or to Friedmann-type (expanding
in all directions) solutions. We also found a new kind of singularity which
arises from the fact that the anisotropic expansion rates are multiple-valued
function of time. The initial singularity in the isotropic limit of this model
belongs to this new kind of singularity. In our analysis the anisotropic
solutions are likely to be singular when the super-inflation is steep.
