  We give a generalization of the duality of a zero-dimensional complete
intersection to the case of one-dimensional almost complete intersections,
which results in a {\em Gorenstein module} $M=I/J$. In the real case the
resulting pairing has a signature, which we show to be constant under flat
deformations. In the special case of a non-isolated real hypersurface
singularity $f$ with a one-dimensional critical locus, we relate the signature
on the jacobian module $I/J_f$ to the Euler characteristic of the positive and
negative Milnor fibre, generalising the result for isolated critical points. An
application to real curves in $\P^2(\R)$ of even degree is given.
