  In this paper we present a generalisation of a theorem due to Cornalba and
Harris, which is an application of Geometric Invariant Theory to the study of
invariants of fibrations.
  In particular, our generalisation makes it possible to treat the problem of
bounding the invariants of general fibred surfaces. As a first application, we
give a new proof of the slope inequality and of a bound for the invariants
associated to double cover fibrations.
