  Mellin transform of fibre integral is calculated for certain classes of
non-degenerate affine complete intersections. The lattice structure of the
poles of the Mellin transform is clarified by means of the mixed Hodge
structure of the affine variety in question. One establishes the relation of
the fibre integral with the hypergeometric function of Horn and that of
Gel'fand-Kapranov-Zelevinski. As an application we prove an hypothesis proposed
by Berglund, Candelas et altri on the mirror symmetry.
