  By means of N-body simulations we study the global dynamics of triplets of
galaxies, considering initial conditions starting from `maximum expansion' and
in virial equilibrium. Unlike previous studies we treat galaxies
self-consistently. We do not consider the influence of a primordial common halo
of dark matter. Our results indicate that a low number of triple mergers are
expected at the present epoch (~10%) for collapsing triplets. Initially
virialised conditions yield ~5% of triple mergers in ~10 Gyr of evolution;
hence, the 3-galaxy problem has stable states. No overmerging problem for these
small groups of galaxies is found. Their geometrical properties, as reflected
by the Agekyan-Anosova map, do not show an excess of extreme hierarchical
triplets. The median velocity dispersion of observed compact triplets (~100
km/s) is not well reproduced in our models at the present epoch. However, about
10% of simulated triplets starting from maximum expansion have dynamical
properties very similar to them. Our median values agree, however, very well
with new data on triples. We find that the median mass estimators performs
somewhat better than the virial mass estimate. The VME underestimates mass by
\~35%. We conclude that Karachentsev's compact triplets probably represent the
most advanced stage of gravitational clustering of initially diffuse triplets.
