  Let (W, S) be a Coxeter system. We investigate combinatorially certain
partial orders, called extended Bruhat orders, on a (W x W)-set W(N,C), which
depends on W, a subset N of S, and a component C of N. We determine the length
of the maximal chains between two elements.
  These posets generalize W equipped with its Bruhat order. They include the (W
x W)-orbits of the Renner monoids of reductive algebraic monoids and of some
infinite dimensional generalizations which are equipped with the partial orders
obtained by the closure relations of the Bruhat and Birkhoff cells. They also
include the (W x W)-orbits of certain posets obtained by generalizing the
closure relation of the Bruhat cells of the wonderful compactification.
