  We combine dissipationless N-body simulations and semi-analytic models of
galaxy formation to study the spatial and kinematic distributions of cluster
galaxies in a LCDM cosmology. We investigate how the star formation rates,
colours and morphologies of galaxies vary as a function of distance from the
cluster centre and compare our results with the CNOC1 survey of galaxies from
15 X-ray luminous clusters in the redshift range 0.18 to 0.55. In our model,
gas no longer cools onto galaxies after they fall into the cluster and their
star formation rates decline on timescales of 1-2 Gyr. Galaxies in cluster
cores have lower star formation rates and redder colours than galaxies in the
outer regions because they were accreted earlier. Our colour and star formation
gradients agree with those those derived from the data. The difference in
velocity dispersions between red and blue galaxies observed in the CNOC1
clusters is also well reproduced by the model. We assume that the morphologies
of cluster galaxies are determined solely by their merging histories.
Morphology gradients in clusters arise naturally, with the fraction of bulge-
dominated galaxies highest in cluster cores. We compare these gradients with
the CNOC1 data and find excellent agreement for bulge-dominated galaxies. The
simulated clusters contain too few galaxies of intermediate bulge-to-disk
ratio, suggesting that additional processes may influence the morphological
evolution of disk-dominated galaxies in clusters. Although the properties of
the cluster galaxies in our model agree extremely well with the data, the same
is not true of field galaxies. Both the star formation rates and the colours of
bright field galaxies appear to evolve much more strongly from redshift 0.2 to
0.4 in the CNOC1 field sample than in our simulations.
