  We use new models of stellar population synthesis to estimate the fraction of
stars formed during the last major bursts of star formation in E/S0 galaxies in
low-redshift clusters ($z\simlt0.4$) from the spectral signatures of
intermediate-age stars. We find that the mass fraction of stars formed in late
bursts in early-type galaxies in clusters must have decreased smoothly with
redshift, from about 8\% at $z\approx1$ to less than 1\% at $z\approx0$. This
result, which we interpret as a constraint on stellar mass added in mergers, is
nearly independent of the assumed ages and morphological types of the
progenitor galaxies prior to the last major bursts of star formation. We then
compute the implied color and 4000 {\AA} break evolution for progenitors of
E/S0 galaxies in clusters at redshifts $0\simlt z\simlt1$. We investigate a
conservative model in which all present-day E/S0 galaxies are assumed to
initially be elliptical galaxies and to then undergo bursts of star formation
at the rate estimated from the signatures of intermediate-age stars at low
redshifts. This model reproduces well the observed spread of colors and 4000
{\AA} breaks of galaxies in high-redshift clusters, but underestimates the
fraction of galaxies in the blue tail of the distribution. Such a discrepancy
may be interpreted as an increasing fraction of spiral galaxies in clusters at
high redshift, as suggested independently by recent {\it HST} observations of
intermediate-redshift clusters. The current data do not seem to require
morphological evolution of cluster galaxies out to $z\sim0.4$, but suggest that
either morphological or strong luminosity evolution might have played a major
role at $z\simgt0.7$.
