  In this paper we focus on the problem of computing the number of moduli of
the so called Severi varieties (denoted by V(|D|, \delta)), which parametrize
universal families of irreducible, \delta-nodal curves in a complete linear
system |D|, on a smooth projective surface S of general type. We determine
geometrical and numerical conditions on D and numerical conditions on \delta
ensuring that such number coincides with dim(V(|D|, \delta). As related facts,
we also determines some sharp results concerning the geometry of some Severi
varieties.
