  In one-loop string effective action, we study a generality of non-singular
cosmological solutions found in the isotropic and homogeneous case. We discuss
Bianchi I and IX type spacetimes. We find that nonsingular solutions still
exist in Bianchi I model around nonsingular flat Friedmann solutions. On the
other hand, we cannot find any nonsingular solutions in Bianchi IX model.
Non-existence of nonsingular Bianchi IX universe may be consistent with the
analysis by Kawai, Sakagami and Soda, i.e. the tensor mode perturbations
against nonsingular flat Friedmann universe are unstable, because Bianchi IX
model can be regarded as a closed Friedmann universe with a single
gravitational wave. So based on these facts, we may conclude the nonsingular
universe is found in isotropic case is generally unstable, a singularity
avoidance may not work in the present model.
