  We study a multi-species spin glass system where the density of each species
is kept fixed at increasing volumes. The model reduces to the
Sherrington-Kirkpatrick one for the single species case. The existence of the
thermodynamic limit is proved for all densities values under a convexity
condition on the interaction. The thermodynamic properties of the model are
investigated and the annealed, the replica symmetric and the replica symmetry
breaking bounds are proved using Guerra's scheme. The annealed approximation is
proved to be exact under a high temperature condition. We show that the replica
symmetric solution has negative entropy at low temperatures. We study the
properties of a suitably defined replica symmetry breaking solution and we
optimise it within a ziggurat ansatz. The generalized order parameter is
described by a Parisi-like partial differential equation.
