We analyse the detailed distribution of star-forming and post-starburs
t members in three distant (z=0.31) galaxy clusters in terms of evolut
ionary sequences that incorporate secondary bursts of star formation o
n pre-existing stellar populations. Using the number density of spectr
oscopically confirmed members of the EW(H delta) versus B - R plane fr
om existing data, and for a larger K'-limited sample on the U-I versus
I-K' plane from newly acquired infrared images, we demonstrate that t
he proportion of cluster members undergoing secondary bursts of star f
ormation during the last similar to 2 Gyr prior to the epoch of observ
ation is probably as high as 30 per cent of the member galaxies. A key
observation leading to this conclusion is the high proportion of H de
lta-strong galaxies in all three clusters. The evolutionary modelling,
whilst necessarily approximate, returns the correct proportions of ga
laxies in various stages of the star formation cycle in terms of both
spectral and colour properties. Hubble Space Telescope (HST) images fo
r the three clusters indicate that a high proportion of the active mem
bers show signs of interaction, whereas the H delta-strong galaxies ap
pear mainly to be regular spheroidals. We examine results from recent
merger simulations in the context of the populations in these clusters
and confirm that the merging of individual galaxies, triggered perhap
s by the hierarchical assembly of rich clusters at this epoch, is cons
istent with the star formation cycle identified in our data. The impli
cations of such a high fraction of active objects in cluster cores are
briefly discussed.