  The nonlocal realistic theory might be the last cornerstone of classical
physics confronting to the quantum theory, which was found mostly untenable in
the bipartite system [Nature 446, 871 (2007)]. We extend the Leggett-type
nonlocal realistic model to arbitrary $N$-partite systems with polarizer
settings, and obtain some stronger inequalities to distinguish quantum
mechanics from nonlocal realistic theories. For illustration, with certain
measurement settings the quantum violations of Leggett-type inequalities are
found for Greenberger-Horne-Zeilinger (GHZ) state. Our results, say the
nonlocal realism in multipartite systems, are testable in experiment.
