We study the 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 the asymptotic past and future with the determinants D = + ∞ and D = 2, respectively. In both scenarios nonsingular trajectories in either the future or the past typically meet the determinant singularity in the past or future when the solutions are singular, apart from the exceptional case where the sign of the time derivative of the dilaton is negative. This implies that the determinant singularity may play a crucial role in leading to singular solutions in an anisotropic background.
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