  Classification theory and the study of projective varieties which are covered
by rational curves of minimal degrees naturally leads to the study of families
of singular rational curves. Since families of arbitrarily singular curves are
hard to handle, it has been shown in a previous paper that there exists a
partial resolution of singularities which transforms a bundle of possibly badly
singular curves into a bundle of nodal and cuspidal plane cubics.
  In cases which are of interest for classification theory, the total spaces of
these bundles will clearly be projective. It is, however, generally false that
an arbitrary bundle of plane cubics is globally projective. For that reason the
question of projectivity seems to be of interest, and the present work gives a
characterization of the projective bundles.
