  A sequence of Bell inequalities for N-particle systems, which involve three
settings of each of the local measuring apparatuses, is derived. For
Greenberger-Horne-Zeilinger states, quantum mechanics violates these
inequalities by factors exponentially growing with N. The threshold
visibilities of the multiparticle sinusoidal interference fringes, for which
local realistic theories are ruled out, decrease as (2/3)^N.
