  We present evidence for bimodal stellar age distribution of pseudobulges of
S0 galaxies as probed by the $D_n(4000)$ index. We do not observe any
bimodality in age distribution for pseudobulges in spiral galaxies. Our sample
is flux limited and contains 2067 S0 and 2630 spiral galaxies drawn from the
Sloan Digital Sky Survey. We identify pseudobulges in S0 and spiral galaxies,
based on the position of the bulge on the Kormendy diagram and their central
velocity dispersion. Dividing the pseudobulges of S0 galaxies into those
containing old and young stellar populations, we study the connection between
global star formation and pseudobulge age on the $u-r$ color-mass diagram. We
find that most old pseudobulges are hosted by passive galaxies while majority
of young bulges are hosted by galaxies which are star forming. Dividing our
sample of S0 galaxies into early-type S0s and S0/a galaxies, we find that old
pseudobulges are mainly hosted by early-type S0 galaxies while most of the
pseudobulges in S0/a galaxies are young. We speculate that morphology plays a
strong role in quenching of star formation in the disc of these S0 galaxies,
which stops the growth of pseudobulges, giving rise to old pseudobulges and the
observed age bimodality.
