  We study linear pencils of curves on normal surface singularities. Using the
minimal good resolution of the pencil, we describe the topological type of
generic elements of the pencil and characterize the behaviour of special
elements. Then we show that the critical locus associated to the pencil is
linked to the special elements. This gives a decomposition of the critical
locus through the minimal good resolution and as a consequence, information on
the topological type of the critical locus.
