The global and local topological zeta functions are singularity invariants associated to a polynomial
f and its germ at 0, respectively. By definition, these zeta functions are rational functions in one variable,
and their poles are negative rational numbers. In this paper we study their poles of maximal possible
order. When f is non-degenerate with respect to its Newton polyhedron, we prove that its local topological
zeta function has at most one such pole, in which case it is also the largest pole; we give a similar result
concerning the global zeta function. Moreover, for any f we show that poles of maximal possible order
are always of the form −1/N with N a positive integer.