We have used deep ground-based imaging in the near-infrared (near-LR) to se
arch for counterparts to the luminous submillimetre (submm) sources in the
catalogue of Small et al, For the majority of the submm sources the near-IR
imaging supports the counterparts originally selected from deep optical im
ages. However, in two cases (10 per cent of the sample) we find a relativel
y bright near-IR source close to the submm position, sources that were unid
entified in the deep Hubble Space Telescope (HST) and ground-based R-band i
mages used by Small et al, We place limits on colours of these sources from
deep high-resolution Keck II imaging and find they have 2 sigma limits-of
(I - K) greater than or similar to 6.8 and (I - K) greater than or similar
to 6.0, respectively. Both sources thus class as extremely red objects (ERO
s), Using the spectral properties of the submm source in the radio and subm
m we argue that these EROs are probably the source of the submm emission, r
ather than the bright spiral galaxies previously identified by Small et al,
This connection provides important insights into the nature of the enigmat
ic ERO population and faint submm galaxies in general. From the estimated s
urface density of these submm-bright EROs we suggest that this class accoun
ts for the majority of the reddest members of the ERO population, in good a
greement with the preliminary conclusions of pointed submm observations of
individual EROs, We conclude that the most extreme EROs represent a populat
ion of dusty, ultraluminous galaxies at high redshifts; further study of th
ese will provide useful insights into the:nature of star formation:in obscu
red galaxies in the early Universe. The:identification of similar counterpa
rts in blank-field submm surveys will be extremely difficult owing to their
faintness (K similar to 20.5, I greater than or similar to 26.5), Finally,
we discuss the radio and submm properties of the two submm-bright EROs dis
covered here and suggest that both galaxies lie at z greater than or simila
r to 2.