We have determined detailed radio spectra for 26 compact sources in the sta
rburst nucleus of M82, between 74 and 1.3 cm. Seventeen show low-frequency
turnovers. One other has a thermal emission spectrum, and we identify it as
an H II, region. The low-frequency turnovers result from absorption by int
erstellar thermal gas in M82. New information on the active galactic nucleu
s candidate 44.01+595 shows it to have a nonthermal falling power-law spect
rum at the highest frequencies and that it is strongly absorbed below 2 GHz
. We derive large magnetic fields in the supernova remnants of order (1-2)(
1 + k)(2/7)phi(-2/7) mG; hence, large pressures in the sources suggest that
the brightest ones are either expanding or are strongly confined by a dens
e interstellar medium. From the largest source in our sample we derive a su
pernova rate of 0.016 yr(-1).