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.
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