  In the 80's D. Eisenbud and J. Harris developed the general theory of limit
linear series, Invent. math. 85 (1986), in order to understand what happens to
linear systems and their ramification points on families of non-singular curves
degenerating to curves of compact type. They applied their theory to the study
of limits of Weierstrass points, among other endeavours. In one of their
articles, Invent. math. 87 (1987), they asked: "What are the limits of
Weierstrass points in families of curves degenerating to stable curves not of
compact type?" In this eprint we address this question within a more general
framework. More precisely, given a family of linear systems on a family of
non-singular curves degenerating to a nodal curve we give a formula for the
limit of the associated ramification divisors in terms of certain limits of the
family of linear systems. In contrast with the theory of limit linear series of
Eisenbud's and Harris', we do not need to blow up the family to swerve the
degenerating ramification points away from the nodes of the limit curve.
Indeed, we can assign the adequate weight to the limit ramification divisor at
any point of the limit curve. In a forthcoming submission we shall deal with
the specific question of limits of Weierstrass points, assuming certain generic
conditions.
