  The nature of the ultra-luminous X-ray sources (ULXs) in the nearby galaxies
is a matter of debates. One of the popular hypothesis associates them with
accretion at a sub-Eddington rate on to intermediate mass black holes. Another
possibility is a stellar-mass black hole in a high-mass X-ray binary accreting
at super-Eddington rates. In this paper we find a highly significant
association between brightest X-ray sources in the Antennae galaxies and
stellar clusters. On the other hand, we show that most of the X-ray sources are
located outside of these clusters. We study clusters associated with the ULXs
using the ESO Very Large Telescope spectra and the Hubble Space Telescope data
together with the theoretical evolutionary tracks and determine their ages to
be below 6 Myr. This implies that the ULX progenitor masses certainly exceed 30
and for some objects are closer to 100 solar masses. We also estimate the ages
of clusters situated close to the less luminous X-ray sources (with luminosity
in the range 3x10^38 < L_X < 10^39 erg/s) and find that most of them are
younger than 10 Myr, because they are surrounded by strong H$\alpha$ emission.
These findings are consistent with the idea that majority of ULXs are massive
X-ray binaries that have been ejected in the process of formation of stellar
clusters by a few-body encounters and at the same time rules out the proposal
that most of the ULXs are intermediate mass black holes.
