  Granato et al(2004) have elaborated a physically grounded model exploiting
the mutual feedback between star-forming spheroidal galaxies and the active
nuclei growing in their cores to overcome, within the hierarchical clustering
scenario for galaxy formation, one of the main challenges facing such scenario,
the fact that massive spheroidal galaxies appear to have formed earlier and
faster than predicted by previous models. Adopting the choice by Granato et al
for the parameters governing the history of the SF,of chemical abundances and
of the gas and dust content of galaxies, we are left with only two parameters
affecting the time and mass dependent SED of spheroidal galaxies. After
complementing the model with a simple description of evolutionary properties of
starburst, normal late-type galaxies and AGNs we have successfully compared the
model with a broad variety of observational data, deep K-band, ISO, IRAS,
SCUBA, radio counts, the corresponding redshift distributions, the IR
background spectrum, and also with data for EROs. We also present detailed
predictions for the GOODS and SWIRE surveys with the Spitzer Space Telescope.
We find that the GOODS deep survey at 24$\mu$m and the SWIRE surveys at 70 and
160$\mu$m are likely to be severely confusion limited. The GOODS surveys in the
IRAC channels are expected to resolve most of the background, to explore the
full passive evolution phase of spheroidal galaxies and most of their active
star-forming phase, detecting galaxies up to z\simeq 4. A substantial number of
high z star-forming spheroidal galaxies should also be detected by the 24\mum
SWIRE and GOODS surveys, while the 70 and 160\mum will be particularly useful
to study the evolution of such galaxies in the range 1 \lsim z \lsim
2.[abridged]
