  Radio and far infrared luminosities of star-forming galaxies follow a tight
linear relation. Making use of ASCA and BeppoSAX observations of a well-defined
sample of nearby star-forming galaxies, we argue that tight linear relations
hold between the X-ray, radio and far infrared luminosities. The effect of
intrinsic absorption is investigated taking NGC3256 as a test case. It is
suggested that the hard X-ray emission is directly related to the Star
Formation Rate. Star formation processes may also account for most of the 2-10
keV emission from LLAGNs of lower X-ray luminosities (for the same FIR and
radio luminosity). Deep Chandra observations of a sample of radio-selected
star-forming galaxies in the Hubble Deep Field North show that the same
relation holds also at high (0.2< z< 1.3) redshift. The X-ray/radio relations
also allow a derivation of X-ray number counts up to very faint fluxes from the
radio Log N-Log S, which is consistent with current limits and models. Thus the
contribution of star-forming galaxies to the X-ray background can be estimated.
