  A great deal of interest has been generated recently by the results of deep
submillimetre surveys, which in principle allow an unobscured view of
dust-enshrouded star formation at high redshift. The extragalactic far-infrared
and submillimetre backgrounds have also been detected, providing further
constraints on the history of star formation. In this paper we estimate the
fraction of these backgrounds and source counts which could be explained by
AGN. The relative fractions of obscured and unobscured objects are constrained
by the requirement that they fit the spectrum of the cosmic X-ray background.
On the assumption that the spectral energy distributions of high redshift AGN
are similar to those observed locally, we find that one can explain at least
10-20 per cent of the 850 micron SCUBA sources at 1mJy and a similar fraction
of the far-infrared/submillimetre background. The exact contribution depends on
the assumed cosmology and the space density of AGN at high redshift (z>3), but
we conclude that active nuclei will be present in a significant (though not
dominant) fraction of the faint SCUBA sources. This fraction could be
significantly higher if a large population of AGN are highly obscured
(Compton-thick) at X-ray wavelengths.
