The asymptotic behavior of the pair correlation functions of a one-dimensional binary mixture of simple model fluids is investigated. The method of investigation is an extension of a technique developed by Fisher and Widom for simple one-component systems. The technique consists of examining the poles of the Laplace transform of the pair correlation function to determine the pole of the least negative real part. The present investigation has been restricted to systems interacting through either hard-sphere or square-well intermolecular pair potentials. In all cases the pair potentials are short-ranged and strictly nearest neighbor.