  Two distant systems can exhibit quantum nonlocality even though the
correlations between them admit a local model. This nonlocality can be revealed
by testing extra correlations between successive measurements on one of the
systems which do not admit a noncontextual model whatever the reduced state of
this system is. This shows that quantum contextuality plays a fundamental role
in quantum nonlocality, and allows an experimental test of the Kochen-Specker
with locality theorem.
