  In order to estimate the masses of the compact, young star clusters in the
merging galaxy pair, NGC 4038/4039 (``the Antennae''), we have obtained medium
and high resolution spectroscopy using ISAAC on VLT-UT1 and UVES on VLT-UT2 of
five such clusters. The velocity dispersions were estimated using the stellar
absorption features of CO at 2.29 microns and metal absorption lines at around
8500 \AA, including lines of the Calcium Triplet. The size scales and light
profiles were measured from HST images. From these data and assuming Virial
equilibrium, we estimated the masses of five clusters. The resulting masses
range from 6.5 x 10^5 to 4.7 x 10^6 M_sun. These masses are large, factor of a
few to more than 10 larger than the typical mass of a globular cluster in the
Milky Way. The mass-to-light ratios for these clusters in the V- and K-bands in
comparison with stellar synthesis models suggest that to first order the IMF
slopes are approximately consistent with Salpeter for a mass range of 0.1 to
100 M_sun. However, the clusters show a significant range of possible IMF
slopes or lower mass cut-offs and that these variations may correlate with the
interstellar environment of the cluster. Comparison with the results of
Fokker-Planck simulations of compact clusters with properties similar to the
clusters studied here, suggest that they are likely to be long-lived and may
lose a substantial fraction of their total mass. This mass loss would make the
star clusters obtain masses which are comparable to the typical mass of a
globular cluster.
