The origin of the far-infrared (FIR)-radio relation observed in active galaxies is investigated. Models developed to calculate the FIR-radio relation expected in starbursts are presented, and their results are compared with samples of radio quiet (RQAG) and radio loud (RLAG) active galaxies. The presence of an active galactic nucleus (AGN) is entered, in bolometric terms, as a function of the energy output generated by a starburst. Pure starbursts, modelled by a continuous star formation process lasting for, at least, 15 million yr, cover the range 6.6>=log(L_FIR/L_rad)>=5.3. Star formation processes characterized by different IMF slopes and mass limits do not greatly affect the value of the FIR-radio relation. The major effect is due to the fraction of energy absorbed and re-emitted by dust. These results would explain in a natural way why spirals follow a universal FIR-radio relation while the observed scatter would be due to variations on the internal extinction from galaxy to galaxy. Pure starburst models reproduce the FIR-radio relation observed in a large fraction of RQAG including starbursts, Seyferts, luminous infrared galaxies and radio quiet quasars (QSOs). However, pure starbursts cannot explain RQAG characterized by log(L_FIR/L_rad) values in the range 5.3 to 4.5. For these RQAG, the contribution of a radio loud AGN (alpha_AGN=L^AGN_FIR/L^AGN_rad>=10^-4), dominating the radio emission output, is required. No pure starburst models can explain the FIR-radio relation observed in radio galaxies and radio loud quasars. The FIR and radio luminosity in RLAG must be originated in a radio loud AGN (10^-3.25<=alpha_AGN<=10^-1.5). Luminous circumnuclear star-forming regions must be present in many of the brightest RQAG, i.e. QSOs. Detection of such circumnuclear star-forming rings in low redshift QSOs with HST would confirm empirically the conclusions presented here.