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 �� 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 �� 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 $z\simgt0.7$.

33 pages, normal TeX