  Radio observations of starburst regions in galaxies have revealed groups of
compact nonthermal sources that may be radiative supernova remnants expanding
in the interclump medium of molecular clouds. Because of the high pressure in
starburst regions, the interclump medium may have a density ~ 10^3 H atoms
cm^{-3} in a starburst nucleus like M82 and ~ 10^4 H atoms cm^{-3} in an
ultraluminous galaxy like Arp 220. In M82, our model can account for the sizes,
the slow evolution, the high radio luminosities, and the low X-ray luminosities
of the sources. We predict expansion velocities ~ 500 km/s, which is slower
than the one case measured by VLBI techniques. Although we predict the remnants
to be radiative, the expected radiation is difficult to detect because it is at
infrared wavelengths and the starburst is itself very luminous; one detection
possibility is broad [OI] 63 micron line emission at the positions of the radio
remnants. The more luminous and compact remnants in Arp 220 can be accounted
for by the higher molecular cloud density. In our model, the observed remnants
lose most of the supernova energy to radiation. Other explosions in a lower
density medium may directly heat a hot, low density interstellar component,
leading to the superwinds that are associated with starburst regions.
