We report on low-resolution multi-object spectroscopy of 30 faint targets (R ~ 24-25) in the HDF-S and AXAF deep field obtained with the VLT Focal Reducer/low dispersion Spectrograph (FORS1). Eight high-redshift galaxies with 2.75< z < 4 have been identified. The spectroscopic redshifts are in good agreement with the photometric ones with a dispersion $sigma_z = 0.07$ at z<2 and $sigma_z = 0.16$ at z>2. The inferred star formation rates of the individual objects are moderate, ranging from a few to a few tens solar masses per year. Five out of the eight high-z objects do not show prominent emission lines. One object has a spectrum typical of an AGN. In the AXAF field two relatively close pairs of galaxies have been identified, with separations of 8.7 and 3.1 proper Mpc and mean redshifts of 3.11 and 3.93, respectively.
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