We present high-resolution échelle 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 ^ { -1 } . By combining with size estimates from Hubble Space Telescope images we infer dynamical masses of 1.3 \times 10 ^ { 7 } M _ { \odot } and 4.0 \times 10 ^ { 6 } M _ { \odot } 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 ( \sim 6 Myr ) and more massive cluster , we detect He ii \lambda 4686 emission of intermediate width , indicating the presence of very massive O-stars . Moreover , analysis of the [ O iii ] \lambda 5007 and H \alpha emission lines from the region near the younger cluster indicates that it is associated with a bubble expanding at \sim 40 km s ^ { -1 } . 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 .