The behaviour of a fluid mixture near a structureless hard wall is investigated. Following earlier work [D. Henderson, F. F. Abraham and J. A. Barker, Molec. Phys.31, 1291 (1976)] we consider the limiting case of a fluid mixture in which one of the species, representing the wall, is dilute and infinitely large. In this limit the Ornstein-Zernike equations yield the density distributions of each of the components with respect to the hard wall. The specific case of a mixture of hard spheres in contact with a hard wall is treated within the Percus-Yevick approximation and explicit results are obtained for a binary mixture. In addition to the density distributions simple expressions are obtained for the integrated densities. The density fluctuations in the fluid near the wall are small and short ranged for the hard sphere fluid. The effects of tails to the interatomic potentials outside the hard spheres can be incorporated approximately and could lead to much larger fluctuations in the densities.