  Autonomous multispecies systems with more-than-two-neighbor interactions are
studied. Conditions necessary and sufficient for closedness of the evolution
equations of the $n$-point functions are obtained. The average number of the
particles at each site for one species and three-site interactions, and its
generalization to the more-than-three-site interactions is explicitly obtained.
Generalizations of the Glauber model in different directions, using generalized
rates, generalized number of states at each site, and generalized number of
interacting sites, are also investigated.
