  We show that the predictions of the recent physical model by Granato et al.
(2001) are fully consistent with the available estimates of the clustering
properties of galaxies at (sub)-mm wavelengths. The model is then exploited to
compute the expected power spectrum of fluctuations due to clustering at the
frequencies of the High Frequency Instrument (HFI) of ESA's {\sc Planck}
satellite. The clustering signal is found to be detectable in regions of low
interstellar dust emission. A further distinctive prediction of the adopted
model is a remarkably high fraction of gravitationally lensed sources at bright
mm/sub-mm fluxes. In fact, according to the adopted model, only thanks to
gravitational lensing, a significant number of high-$z$ forming spheroidal
galaxies will be detectable by large area, shallow surveys at mm/sub-mm
wavelengths, such as those carried out by P{\sc lanck}/HFI. Allowing for other
source populations, we find that the fraction of gravitationally lensed sources
at bright mm/sub-mm fluxes is expected to be up to $\simeq 40%$.
