  We present high-resolution echelle spectroscopy, obtained with the UVES
spectrograph on ESO/VLT, of two luminous star clusters in the metal-poor blue
compact galaxy ESO 338-IG04 at a distance of 37.5 Mpc. Cross-correlating with
template stars, we obtain line-of-sight velocity dispersions of 33 and 17 km/s.
By combining with size estimates from Hubble Space Telescope images we infer
dynamical masses of 1.3x10^7 and 4.0x10^6 solar masses for the two clusters,
making them among the most massive known. The less massive cluster is the
faintest cluster for which a dynamical mass has yet been obtained. In both
clusters we detect Balmer absorption lines which we use to estimate their ages.
  From the younger (~6 Myr) and more massive cluster, we detect He II 4686
emission of intermediate width, indicating the presence of very massive
O-stars. Moreover, analysis of the [O III] 5007 and H-alpha emission lines from
the region near the younger cluster indicates that it is associated with a
bubble expanding at ~40 km/s. We also see from the Na I D absorption lines
indications of neutral gas flows towards the younger cluster. We compare the
dynamical masses with those derived from photometry and discuss implications
for the stellar initial mass function (IMF) in each cluster. Both clusters are
compatible with rather normal IMFs which will favour their long-term survival
and evolution into massive bona fide globular clusters.
