Oblique poles of $int_X| {f}| ^{2lambda}| {g}|^{2mu} square$

Existence of oblique polar lines for the meromorphic extension of the current valued function $int |f|^{2lambda}|g|^{2mu}square$ is given under the following hypotheses: $f$ and $g$ are holomorphic function germs in $CC^{n+1}$ such that $g$ is non-singular, the germ $S:=ens{d fwedge d g =0}$ is one dimensional, and $g|_S$ is proper and finite. The main tools we use are interaction of strata for $f$ (see cite{B:91}), monodromy of the local system $H^{n-1}(u)$ on $S$ for a given eigenvalue $exp(-2ipi u)$ of the monodromy of $f$, and the monodromy of the cover $g|_S$. Two non-trivial examples are completely worked out.