  We study nature of singularities in anisotropic string-inspired cosmological
models in the presence of a Gauss-Bonnet term. We analyze two string gravity
models-- dilaton-driven and modulus-driven cases-- in the Bianchi type-I
background without an axion field. In both scenarios singularities can be
classified in two ways- the determinant singularity where the main determinant
of the system vanishes and the ordinary singularity where at least one of the
anisotropic expansion rates of the Universe diverges. In the dilaton case,
either of these singularities inevitably appears during the evolution of the
system. In the modulus case, nonsingular cosmological solutions exist both in
asymptotic past and future with determinant $D=+\infty$ and D=2, respectively.
In both scenarios nonsingular trajectories in either future or past typically
meet the determinant singularity in past/future when the solutions are
singular, apart from the exceptional case where the sign of the time-derivative
of dilaton is negative. This implies that the determinant singularity may play
a crucial role to lead to singular solutions in an anisotropic background.
