galaxy fluxes at almost all wavelengths, from X to microwaves. On the contrary, in early-type galaxies where the current star formation rate has faded out the X-FIR fluxes link disappears. This result obtained for early-type galaxies is discussed and explained in detail in the frame of a suitable theoretical model, obtained coupling chemo-dynamical N-body simulations with a dusty spectrophotometric code of population synthesis.]{}

Introduction
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The observations of galaxies at various wavelengths, going from radio to X-ray, allow to study the relationships existing between the various phases of the interstellar gas, and between gas, dust and stars. Some of these relations are already known since many years, such as that between CO and far infrared (FIR) luminosities [@mirabel; @sanders; @solomon; @devereux]. Others, connected with X-ray emission, have been studied more recently [@padovani; @david; @ranalli].

At present, different tracers of the gas are known, such as millimetric lines for the cold molecular gas, the 21 cm line for atomic hydrogen at $\sim$100 K, IR bands for molecules at thousands of degrees, UV lines and X-ray emission for hotter gas. The dust distribution is traced also by FIR emission at 60 and 100 $\mu$m if the grains are warm [@bregman] or at 