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 NGC 3256 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 ($0.2\la z\la 1.3$) 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.