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 zsimeq 4. A substantial number of high z star-forming spheroidal galaxies should also be detected by the 24mum SWIRE and GOODS surveys, while the 70 and 160mum will be particularly useful to study the evolution of such galaxies in the range 1 lsim z lsim 2.[abridged]
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