Integral field spectroscopy in the K band (1.9-2.4 mum) was performed on fo
ur IR-bright star clusters and the two nuclei in NGC 4038/4039 ("the Antenn
ae II). Two of the clusters are located in the overlap region of the two ga
laxies and together comprise approximate to 25% of the total 15 mum emissio
n of the total 4.8 GHz emission from this pair of merging galaxies. The oth
er two clusters, each of them spatially resolved into two components, are l
ocated in the northern galaxy, one in the western and one in the eastern lo
op of blue clusters. Comparing our analysis of Br gamma, CO band heads, He
I 2.058 mum, H alpha (from archival Hubble Space Telescope data), and V-K c
olors to stellar population synthesis models indicates that the clusters ar
e extincted (A(v) approximate to 0.7-4.3 mag) and young, displaying a signi
ficant age spread (4-13 Myr). The starbursts in the nuclei are much older (
65 Myr), with the nucleus of NGC 4038 displaying a region of recent star fo
rmation northward of its K-band peak. Using our derived age estimates and a
ssuming the parameters of the initial mass function (Salpeter slope, upper
mass cutoff of 100 M-., Miller-Scalo between 1 and 0.1 M-.), we find that t
he clusters have masses between 0.4 x 10(6) and 3 x 10(6) M-..