  We present a method based on two broad-band colors to investigate the nature
of the Extremely Red Objects (EROs), i.e., the galaxies selected to have very
red optical-to-infrared colors. Dusty starburst and old ellipticals at
redshifts between 1 and 2 appear to occupy two different regions of the J-K vs.
I-K color diagram, allowing for an easy classification. This diagnostic was
applied to a complete sample of 57 EROs: the two populations are found to be
present in the sample in similar abundances. The cosmic star formation density
in the dusty starbursts is found to be of the order of that in the Lyman-Break
Galaxies.
