Aims.Although S0 galaxies are usually thought to be “red and dead”, they often demonstrate star formation that is organized in ring structures. We try to clarify the nature of this phenomenon and its difference from star formation in spiral galaxies. Two early-type galaxies with outer rings, NGC 6534 and MCG 11-22-015, were selected to be studied.Methods.After inspecting the gas excitation in the rings using the Baldwin–Phillips–Terlevich method, we estimated the star formation rates (SFR) in the two outer rings of our galaxies using several SFR indicators derived from narrow-band photometry in the Hαemission line and archival GALEX ultraviolet images of the galaxies.Results.The ionized gas is excited by young stars in the ring of NGC 6534 and partly by shocks in MCG 11-22-015. The oxygen abundances in the HII regions of the rings are close to solar. The derived SFRs allow us to qualitatively restore star formation histories (SFH) in the rings: in NGC 6534, the SFH has been flat during the last 100–200 Myr, and in MCG 11-22-015, the star formation has started only a few Myr ago. We suggest that the rings in NGC 6534 and MCG 11-22-015 have different natures: the former is a resonant ring supplied with gas perhaps through tidal effects, and the latter has been produced by a satellite accretion. Recent outer gas accretion is implied in both cases.