  Though S0 galaxies are usually thought to be `red and dead', they often
demonstrate star formation 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,
are selected to be studied. 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. We estimate the
star formation rates (SFR) in the two outer rings of the galaxies by using
several SFR indicators derived from narrow-band photometry in the H-alpha
emission line and archival GALEX ultraviolet images of the galaxies. The
derived SFRs allow to qualitatively restore star formation histories (SFH) in
the rings: in NGC 6534 the SFH is 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 one 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.
