  We present a comprehensive analysis of the stellar population properties
(age, metallicity and the alpha-element enhancement [E/Fe]) and morphologies of
red-sequence galaxies in 24 clusters and groups from z~0.75 to z~0.45. The
dataset, consisting of 215 spectra drawn from the ESO Distant Cluster Survey,
constitutes the largest spectroscopic sample at these redshifts for which such
an analysis has been conducted. Analysis reveals that the evolution of the
stellar population properties of red-sequence galaxies depend on their mass:
while the properties of most massive are well described by passive evolution
and high-redshift formation, the less massive galaxies require a more extended
star formation history. We show that these scenarios reproduce the index-sigma
relations as well as the galaxy colours. The two main results of this work are
(1) the evolution of the line-strength indices for the red-sequence galaxies
can be reproduced if 40% of the galaxies with sigma < 175 km/s entered the
red-sequence between z=0.75 to z=0.45, in agreement with the fraction derived
in studies of the luminosity functions, and (2) the percentage the red-sequence
galaxies exhibiting early-type morphologies (E and S0) decreases by 20% from
z=0.75 to z=0.45. This can be understood if the red-sequence gets populated at
later times with disc galaxies whose star formation has been quenched. We
conclude that the processes quenching star formation do not necessarily produce
a simultaneous morphological transformation of the galaxies entering the
red-sequence.
