  We analyze a class of exact type II solutions of the Robinson-Trautman family
which contain pure radiation and (possibly) a cosmological constant. It is
shown that these spacetimes exist for any sufficiently smooth initial data, and
that they approach the spherically symmetric Vaidya-(anti-)de Sitter metric. We
also investigate extensions of the metric, and we demonstrate that their order
of smoothness is in general only finite. Some applications of the results are
outlined.
