  The structure of the Einstein field equations describing the gravitational
collapse of spherically symmetric isotropic fluids is analyzed here for general
equations of state. A suitable system of coordinates is constructed which
allows us, under a hypothesis of Taylor-expandability with respect to one of
the coordinates, to approach the problem of the nature of the final state
without knowing explicitely the metric. The method is applied to investigate
the singularities of linear barotropic perfect fluids solutions and to a family
of accelerating fluids.
