  The two-loop (order $\alpha'$) $\beta$-function equations, which are
equivalent to the equations of motion of $\alpha'$-corrected string effective
action, are considered for anisotropic homogeneous space-times. These equations
are solved for all Bianchi-type models in two schemes of effective action,
namely $R^2$ and Gauss-Bonnet schemes with zero cosmological constant and then
the metric, dilaton and $B$-field are found at $\alpha'$ perturbative
corrections.
