We present the results of VLT optical spectroscopy of a complete sample of 78 EROs with R-Ksgeq5 over a field of 52 arcmin^2. About 70% of the 45 EROs with Ksleq19.2 have been spectroscopically identified with old passively evolving and dusty star-forming galaxies at 0.7<z<1.5. The two classes are about equally populated and for each of them we present and discuss the average spectrum. From the old ERO average spectrum and for Z=Z_{odot} we derive a minimum age of sim 3 Gyr, corresponding to a formation redshift of z_f gtsima 2.4. PLE models with such formation redshifts well reproduce the density of old EROs (consistent with being passively evolving ellipticals), whereas the predictions of the current hierarchical merging models are lower than the observed densities by large factors (up to an order of magnitude). From the average spectrum of the star-forming EROs we estimate a substantial dust extinction with E(B-V) gtsima 0.5. The star formation rates, corrected for the average reddening, suggest a significant contribution from EROs to the cosmic star-formation density at z sim 1.