  The nature of the galaxies that give rise to absorption lines, such as damped
Lyman-alpha systems (DLAs) or strong MgII lines, in quasar spectra is difficult
to investigate in emission. Taking advantage of the total absorption of the QSO
light bluewards of the Lyman limit of two DLAs at z>3.4, we look for the
continuum emission from intervening galaxies at z~2 that are identified via
strong metal absorption lines. The MgII absorbers have equivalent width large
enough to be potential DLA systems. Deep images are obtained with the FOcal
Reducer and Spectrograph (FORS1) on the Very Large Telescope for the fields
towards SDSS J110855+120953 and SDSS J140850+020522. These quasars have MgII
absorption lines at z=1.87 (W_r(MgII)=2.46 A) and z=1.98 (W_r(MgII)=1.89 A),
respectively, and each QSO has two intervening higher redshift DLAs at z>3. The
U and R bands of FORS1 lie blue and redwards of the Lyman limit of the
background DLAs, allowing us to search for emission from the foreground
galaxies directly along the lines of sight to the QSOs. No galaxies are found
close to the sight line of the QSO to a point source limit of U_AB=28.0. In
both fields, the closest objects lie at an impact parameter of 5 arcsec
corresponding to 40 kpc in projection at z=2, and have typical colours of star
forming galaxies at that redshift. However, the currently available data do not
allow us to confirm if the galaxies lie at the same redshifts as the absorption
systems. A more extended structure is visible in the SDSS J14085+020522 field
at an impact parameter of 0.8 arcsec or 7 kpc. If these objects are at z~2
their luminosities are 0.03-0.04 L* in both fields. The star formation rates
estimated from the UV flux are 0.5-0.6 M_sun yr^-1. (Abbreviated).
