  We use the semi-analytic models of galaxy formation developed by Kauffmann,
White \& Guiderdoni to generate predictions for the observed properties of
cluster and group galaxies at redshifts between 0 and 0.6. We examine four sets
of cosmological initial conditions: low-density CDM models with and without
cosmological constant, a flat CDM model and a mixed dark matter model. These
models were selected because they span a wide range in cluster formation epoch.
The semi-analytic models that we employ are able to follow both the evolution
of the dark matter component of clusters and the formation and evolution of the
stellar populations of the cluster galaxies. We are thus able to generate model
predictions that can be compared directly with the observational data. In the
low-density CDM models, clusters form at high red- shift and accrete very
little mass at recent times. Our models predict that essentially no evolution
in the observed properties of clusters will have occurred by a redshift of 0.6,
in direct contradiction with the data. In contrast, in the MDM model, both
galaxies and clusters form extremely late. This model predicts evolution which
appears to be too extreme to be in agreement with the observations. The flat
CDM model, which is intermediate in structure formation epoch, is most
successful. This model is able to account for the evolution of the blue
fraction of rich clusters with redshift, the relationship between blue fraction
and cluster richness at different epochs, and the changes in the distribution
of the morphologies of cluster galaxies by a redshift of 0.4.
