The selection and the observations of the ERO sample were made in the context of the K20 survey (http://www.arcetri.astro.it/~k20/). The prime aim of such a survey is to derive the redshift distribution of about 550 K-selected objects with $Ks\leq 20$ in order to constrain the galaxy formation models. The targets were selected from a 32.2 arcmin² area of the Chandra Deep Field South (CDFS; Giacconi et al. 2001) using the images from the ESO Imaging Survey public database (EIS; http://www.eso.org/science/eis/; the R- and the Ks-band images were reduced and calibrated by the EIS team and by our group respectively), and from a 19.8 arcmin² field centered at 0055-269 using NTT+SOFI and VLT-UT2+FORS2 Ks- and R-band images respectively (Fontana et al., in preparation). More details on the photometry will be given in forthcoming papers. From the total sample with $Ks\leq20.0$ , we extracted the subsample of EROs with $R-Ks\geq5.0$ , with the colors measured in 2 $^{\prime\prime}$ arcsec diameter corrected aperture to match the color definition of D00. The total sample includes 78 EROs, corresponding to a surface density of 1.50 $\pm$ 0.17 arcmin^-2, consistent with that of Thompson et al. (1999) (1.88 $\pm$ 0.11 arcmin^-2 over a field of 154 arcmin²). The ratio between the number of EROs and the total number of objects at $Ks\leq19.2$ is 0.134 $\pm$ 0.021, consistent with the value of 0.127 $\pm$ 0.006 of D00.

Multi-object spectroscopy of EROs was made with the ESO VLT UT1 and UT2 equipped with FORS1 (October-November 1999) and FORS2 (November 2000) during 0.5 $^{\prime\prime}$ -1.5 $^{\prime\prime}$ seeing conditions and with 0.7 $^{\prime\prime}$ -1.2 $^{\prime\prime}$ wide slits depending on the seeing. The grisms 150I, 200I, 300I were used with typical integration times of 1-3 hours. Dithering of the targets along the slits between two fixed positions was made for most observations in order to efficiently remove the CCD fringing and the strong OH sky lines at $\lambda_{\rm obs}>7000$ Å. The spectra were calibrated using standard spectrophotometric stars, dereddened for atmospheric extinction, corrected for telluric absorptions and scaled to the total R-band magnitudes.

Table 1: The ERO spectroscopic identifications.
Sample $N_{\rm tot}$ $N_{\rm id}$ $N_{\rm u}$ $N_{\rm old}$ $N_{\rm sf}$ $N(\rm ambig)$

$Ks\leq20.0$ 78 35 43 15 18 2

$Ks\leq19.2$ 45 30 15 14 15 1

Sample	$N_{\rm tot}$	$N_{\rm id}$	$N_{\rm u}$	$N_{\rm old}$	$N_{\rm sf}$	$N(\rm ambig)$

$Ks\leq20.0$	78	35	43	15	18	2
$Ks\leq19.2$	45	30	15	14	15	1

2 The K20 ERO sample