  (Abridged) This paper predicts self-consistent faint galaxy counts from the
UV to the submm wavelength range. The STARDUST spectral energy distributions
described in Devriendt et al. (1999) are embedded within the explicit
cosmological framework of a simple semi-analytic model of galaxy formation and
evolution. We build a class of models which capture the luminosity budget of
the universe through faint galaxy counts and redshift distributions in the
whole wavelength range spanned by our spectra. In contrast with a rather stable
behaviour in the optical and even in the far-IR, the submm counts are
dramatically sensitive to variations in the cosmological parameters and changes
in the star formation history. Faint submm counts are more easily accommodated
within an open universe with a low value of $\Omega_0$, or a flat universe with
a non-zero cosmological constant. This study illustrates the implementation of
multi-wavelength spectra into a semi-analytic model. In spite of its
simplicity, it already provides fair fits of the current data of faint counts,
and a physically motivated way of interpolating and extrapolating these data to
other wavelengths and fainter flux levels.
