  In [8], M.Daumens and M.Perroud studied a two Galilean free particles system
by realizing the three dimensional Galilei group on its maximal coadjoint
orbit. In this paper we realize a similar study for the one spatial dimesnional
Galilei group. As its maximal coadjoint orbit describes a non free massive
particle [6], this gives us a two non free galilean partcles system. Use of the
barycenter coordinates gives rise to the notions of a total force and a
relative force similar to those of a total linaer momentum and a relative
linear momentum ([]8),[9],[10]). We will distinguish the case of a non isolated
system from that of an isolated one. We will show that the barycenter is
accelerated in the first case while it moves with a constant velocity in the
second one.
