  It is shown that compact groups of galaxies (HCGs, ShCGS) are stable
formations, in which principal member galaxies together with faint galaxies in
their environment rotate in elongated orbits around the common gravitational
center of the group. Hence, the multitude of puzzles related to CGs: the very
existence of CGs, absence of strong radio sources, absence of strong signs of
interaction and merging, the fact that elliptical members (the best candidates
for ongoing merging) are not more frequently first-ranked than spirals, etc.,
are solved. The number of such groups, may be much higher in the near Universe,
since only those of them, the elongation of which is oriented close to the line
of sight, or bright members of which happen to be close to each other during
regular rotation, are detected as the so-called compact groups.
