  We present results on number counts of Extremely Red Objects (EROs) in a 2850
arcmin^2 near-infrared survey performed in European Large Area ISO Survey
(ELAIS) fields at K<17.5. Counts of EROs are extended to brighter levels than
available previously, giving 0.002 +/- 0.001 arcmin^-2 at K<16.5 and consistent
numbers with literature values at fainter magnitudes. Photometric redshifts
from HYPERZ as well as GRASIL model SEDs of galaxies imply that our EROs are
located in the range z=0.7-1.5, with the bulk of the population at z~1. Taking
advantage of the ISO data in the fields, we use mid-IR detections to constrain
the number of dusty EROs, and also discuss the superior capabilities of Spitzer
Space Telescope to detect dusty EROs. Both the mid-IR data and the use of
colour-colour diagrammes indicate that at most 10-20% of the EROs in this
bright regime are dusty starbursting systems. The space density of our EROs,
interpreted to be counterparts of local >2-3L^star massive galaxies at around
z~1, is estimated to be approx. 2x10^-5 Mpc^-3, which is consistent with local
values. Furthermore, the cumulative number counts at our bright magnitudes are
remarkably well fitted by pure luminosity evolution models.
