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(abridged) Strongly star-forming galaxies of subsolar metallicities aretypical of the high-redshift universe. Here we therefore provide accurate datafor two low-z analogs, the well-known low-metallicity emission-line galaxiesHaro 11 and ESO 338-IG 004. On the basis of Very Large Telescope/X-shooterspectroscopic observations in the wavelength range 3000-24000\AA, we usestandard direct methods to derive physical conditions and element abundances.Furthermore, we use X-shooter data together with Spitzer observations in themid-infrared range to attempt to find hidden star formation. We deriveinterstellar oxygen abundances of 12 + log O/H = 8.33+/-0.01, 8.10+/-0.04, and7.89+/-0.01 in the two HII regions B and C of Haro 11 and in ESO 338-IG 004,respectively. The observed fluxes of the hydrogen lines correspond to thetheoretical recombination values after correction for extinction with a singlevalue of the extinction coefficient C(Hbeta) across the entire wavelength rangefrom the near-ultraviolet to the NIR and mid-infrared for each of the studiedHII regions. Therefore there are no emission-line regions contributing to theline emission in the NIR range, which are hidden in the optical range. Theagreement between the extinction-corrected and CLOUDY-predicted fluxes impliesthat a HII region model including only stellar photoionisation is able toaccount for the observed fluxes, in both the optical and NIR ranges. Allobserved spectral energy distributions (SEDs) can be reproduced quite wellacross the whole wavelength range by model SEDs except for Haro 11B, wherethere is a continuum flux excess at wavelengths >1.6mum. It is possible thatone or more red supergiant stars are responsible for the NIR flux excess inHaro 11B. We find evidence of a luminous blue variable (LBV) star in Haro 11C.

VLT/X-shooter observations of blue compact galaxies Haro 11 and ESO 338-IG 004