  We analyze the structure of correlations among more than two quantum systems.
We introduce a classification of correlations based on the concept of
non-separability, which is different {\em a priori} from the concept of
entanglement. Generalizing a result of Svetlichny [Phys. Rev. D {\bf 35} (1987)
3066] on 3-particle correlations, we find an inequality for $n$-particle
correlations that holds under the most general separability condition and that
is violated by some quantum-mechanical states.
