The feasibility of using near-infrared observations to discover supernovae
in the nuclear and circumnuclear regions of nearby starburst galaxies is in
vestigated. We provide updated estimates of the intrinsic core-collapse sup
ernova rates in these regions. We discuss the problem of extinction, and pr
esent new estimates of the extinction towards 33 supernova remnants in the
starburst galaxy M 82. This is done using H I and H-2 column density measur
ements. We estimate the molecular to atomic hydrogen mass ratio to be 7.4 /- 1.0 in M 82. We have assembled near-infrared photometric data for a tota
l of 13 core-collapse supernovae, some unpublished hitherto. This constitut
es the largest database of infrared light curves for such events. We show t
hat the infrared light curves fall into two classes, 'ordinary' and 'slowly
declining'. Template JHKL light curves are derived for both classes. For o
rdinary core-collapse supernovae, the average peak JHKL absolute magnitudes
are -18.4, -18.6, -18.6 and -19.0 respectively. The slowly declining core-
collapse supernovae are found to be significantly more luminous than the or
dinary events, even at early times, having average peak JHKL absolute magni
tudes of -19.9, -20.0, -20.0 and -20.4 respectively. We investigate the eff
iciency of a computerized image subtraction method in supernova detection.
We then carry out a Monte Carlo simulation of a supernova search using K-ba
nd images of NGC 5962. The effects of extinction and observing strategy are
discussed. We conclude that a modest observational programme will be able
to discover a number of nuclear supernovae.