  HST observations reveal that young massive star clusters form in gas-rich
environments like the Antenn{\ae} galaxy which will merge in collisional
processes to form larger structures. These clusters amalgamate and if some of
these clusters harbour a massive black hole in their centres, they can become a
strong source of gravitational waves when they coalesce. In order to understand
the dynamical processes that are into play in such a scenario, one has to
carefully study the evolution of the merger of two of such young massive star
clusters and more specifically their respective massive black holes. This will
be a promising source of gravitational waves for both, LISA and the proposed
Big Bang Observer (BBO), whose first purpose is to search for an
inflation-generated gravitational waves background in the frequency range of
$10^{-1}-1$ Hz. We used high-resolution direct summation $N-$body simulations
to study the orbital evolution of two colliding globular clusters with
different initial conditions. Even if the final eccentricity is almost
negligible when entering the bandwidth, it will suffice to provide us with
detailed information about these astrophysical events.
