  n a number of papers it was shown that there are one-dimensional systems such
that they contain solutions with, so called, overcompressive singular shock
waves besides the usual elementary waves (shock and rarefaction ones as well as
contact discontinuities). One can see their definition for a general 2 $\times$
2 system with fluxes linear in one of dependent variables in \cite{Ned1}. This
paper is devoted to examining their interactions with themselves and elementary
waves. After a discussion of systems given in a general form, a complete
analysis will be given for the ion-acoustic system.
