  The stability analysis of an anisotropic inflationary universe of the four
dimensional Neveu-Schwarz--Neveu-Schwarz string model with a nonvanishing
cosmological constant is discussed in this paper. The accelerating expansion
solution found earlier is shown to be stable against the perturbations with
respect to the dilaton and axion fields once the dilaton field falls close to
the local minimum of the symmetry-breaking potential. This indicates that the
Bianchi I space tends to evolve to an isotropic flat Friedmann-Robertson-Walker
space. This expanding solution is also shown to be stable against the
perturbation with respect to anisotropic spatial directions.
