It has been shown (Maffei 1996) that, owing to the steep submillimetre
spectrum of galaxies, the background fluctuations due to unresolved
sources can be dominated by sources much weaker than the detection
limit. Based on the models described above, the variance of the
fluctuations of the extragalactic background are lower by about an
order of magnitude than that of dust even for the maximal model (PLE)
which reproduces the isotropic component. The multi-frequency
information will allow an accurate subtraction of this small
component from the millimetre wavelength PLANCK maps, in order to
measure CMB anisotropies. Nevertheless, integrated information on
fainter, high-redshift objects could be extracted from the all-sky
PLANCKby means of an analysis of the small-scale anisotropies at
m, in clean regions of the sky where Galactic dust
does not mask this information. This sample will set stringent constraints
on the source counts to flux levels
a few mJy. At these flux levels,
we may test, in particular, the anisotropy signal expected from a
population of high-redshift, dusty primeval spheroids, which may be
responsible for the rather high isotropic background in the
COBE-FIRAS data (Puget et al. 1995). The presence or absence of
such a signal will provide a further strong constraint on models
of galaxy formation and evolution.