  For a generic (polynomial) one-parameter deformation of a complete
intersection, there is defined its monodromy zeta-function. We provide explicit
formulae for this zeta-function in terms of the corresponding Newton polyhedra
in the case the deformation is non-degenerate with respect to its Newton
polyhedra. Using this result we obtain the formula for the monodromy
zeta-function at the origin of a polynomial on a complete intersection, which
is an analog of the Libgober--Sperber theorem.
