  In this paper I focus on three topics related to the dynamical evolution of
small galaxy groups, for which the input of N-body simulations has been
decisive. These are the merging rates in compact groups, the properties of
remnants of multiple mergers, and the evolution of disc galaxies surrounded by
one or more satellites. The short dynamical times of compact groups make it
difficult to understand why such groups are observed at all. N-body simulations
have pointed out two possible classes of solutions to this problem. The first
one proposes that there is on-going formation of compact groups, or that the
longevity of the group is due to secondary infall. For the second class of
solutions the longevity of compact groups is due either to their specific
initial conditions, or to a massive common halo, encompassing the whole group.
I discuss here these alternatives, together with their respective advantages
and disadvantages. I then turn to the structure of remnants of multiple mergers
and compare the results of N-body simulations with the properties of observed
elliptical galaxies. Finally I discuss the dynamical evolution of a disc galaxy
surrounded by one or more spherical satellites.
