  In this paper we review the present status of the piNNN--NNN problem. In
particular, we re-consider the chain-labelled approach recently proposed by us,
and identify a class of graphs, previously overlooked, which prevents the
kernel of the corresponding piNNN--NNN equations from being connected. We
propose some pproximate schemes, yielding connected-kernel equations. A
generalization of the residue method allows to relate the transition amplitudes
for the coupled piNNN--NNN system to the chain-labelled formalism. The
quasi-particle approach is extended to the present situation, where
emission/absorption of particles is allowed. The open problems for the
piNNN--NNN system in the light of the present and of previous approaches are
finally discussed.
