Deep imaging and spectroscopy have been carried out for optical counterparts of a sample of 68 faint radio sources (S > 0.2 mJy) in the Marano Field. About 60 per cent of the sources have been optically identified on deep CCD exposures (limit R ≃ 24.0) or ESO 3.6-m plates (limit bJ≃ 22.5). 34 spectra (50 per cent of the total radio sample) were obtained with the ESO 3.6-m telescope and 30 redshifts were determined. In addition to a few broad-line active galactic nuclei, three main spectroscopic classes have been found to dominate the faint radio galaxy population. (1) Early-type galaxies (without emission lines in their spectra) having 0.1 < z < 0.8 and covering the range of radio fluxes 0.2--30 mJy. (2) Late-type galaxies (with narrow emission lines in their spectra) at moderate redshift (z < 0.4), with relatively bright magnitudes (B < 22.5) and sub-mJy radio fluxes. When applicable, the diagnostic diagrams for these sources are consistent with the lines being produced by star-formation activity. (3) A group of bright high-redshift (z > 0.8) radio galaxies with moderate-to-strong [O ii] emission. All of them have B > 22.5 and most of them have S1.4 GHz > 1 mJy. They have spectra, colours and absolute magnitudes similar to those of the classical bright elliptical radio galaxies found in surveys carried out at higher radio fluxes. Star-forming galaxies do not constitute the main population of our radio sources identified with galaxies. In fact, even at sub-mJy level the majority of our radio sources are identified with early-type galaxies. This apparent discrepancy with previous results is due to the fainter magnitude limit reached in our spectroscopic identifications. Moreover, using mainly the large radio-to-optical ratio and the information from the available limits on the optical magnitudes of the unidentified radio sources, we conclude that the great majority of them are likely to be early-type galaxies, at z > 1. If correct, it would suggest that the evolution of the radio luminosity function of spiral galaxies, including starbursts, might not be as strong as suggested in previous evolutionary models.