  We study the gravitational collapse of a generalised Vaidya spacetime in the
context of the Cosmic Censorship hypothesis. We develop a general mathematical
framework to study the conditions on the mass function so that future directed
non-spacelike geodesics can terminate at the singularity in the past. Thus our
result generalises earlier works on gravitational collapse of the combinations
of Type-I and Type-II matter fields. Our analysis shows transparently that
there exist classes of generalised Vaidya mass functions for which the collapse
terminates with a locally naked central singularity. We calculate the strength
of the these singularities to show that they are strong curvature singularities
and there can be no extension of spacetime through them.
