A handful of nearby supernovae (SNe) with visual extinctions of a few magnitudes have recently been discovered. However, an undiscovered population of much more highly extinguished ( AV>10) core-collapse supernovae (CCSNe) is likely to exist in the nuclear (central kiloparsec) regions of starburst galaxies. The high dust extinction means that optical searches for such SNe are unlikely to be successful. Here, we present preliminary results from our ongoing near-infrared Ks-band search programme for nuclear SNe in nearby starburst galaxies. We also discuss searches for SNe in luminous and ultraluminous infrared galaxies.