  The feasibility of using near-infrared observations to discover supernovae in
the nuclear and circumnuclear regions of nearby starburst galaxies is
investigated. We provide updated estimates of the intrinsic core-collapse
supernova rates in these regions. We discuss the problem of extinction, and
present 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
measurements. 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 total of
13 core-collapse supernovae, some unpublished hitherto. This constitutes the
largest database of IR light curves for such events. We show that the IR light
curves fall into two classes, ``ordinary'' and ``slow-declining''. Template
JHKL light curves are derived for both classes. For ordinary core-collapse
supernovae, the average peak JHKL absolute magnitudes are -18.4, -18.6, -18.6,
and -19.0 respectively. The slow-declining core-collapse SNe are found to be
significantly more luminous than the ordinary events, even at early times,
having average peak JHKL absolute magnitudes of -19.9, -20.0, -20.0, and -20.4
respectively. We investigate the efficiency of a computerised image subtraction
method in supernova detection. We then carry out a Monte Carlo simulation of a
supernova search using K-band 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.
