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.