By undertaking deep long-slit spectroscopy with the focal reducer Spectral Camera with Optical Reducer for Photometrical and Interferometrical Observations (SCORPIO) of the Russian 6 m telescope, we studied stellar population properties and their variation with radius in 15 nearby S0 galaxies sampling a wide range of luminosities and environments. For the large-scale stellar discs of S0s, we have measured simple stellar population (SSP)-equivalent metallicities ranging from the solar one down to [ Z/H ]=−0.4 to −0.7, rather high magnesium-to-iron ratios, [Mg/Fe] ≥ +0.2, and mostly old SSP-equivalent ages. Nine of 15 (60 ± 13 per cent) galaxies have large-scale stellar discs older than 10 Gyr, and among those we find all the galaxies which reside in denser environments. The isolated galaxies may have intermediate-age stellar discs which are 7–9 Gyr old. Only two galaxies of our sample, NGC 4111 and NGC 7332, reveal SSP-equivalent ages of their discs of 2–3 Gyr. Just these two young discs appear to be thin, while the other, older discs have scale heights typical for thick stellar discs. The stellar populations in the bulges at radii of 0.5re are on the contrary more metal rich than the solar Z⊙, with the ages homogeneously distributed between 2 and 15 Gyr, being almost always younger than the discs. We conclude that S0 galaxies could not form in groups at z ≈ 0.4 as is thought now; a new scenario of the general evolution of disc galaxies is proposed instead.