Gamma-ray observations of the nearby starburst galaxies NGC 253 and M82 over the energy range (0.05-10) MeV have been obtained with the Oriented Scintillation Spectrometer Experiment (OSSE) spectrometer on the Compton Gamma-Ray Observatory (CGRO). The priority of these galaxies as OSSE targets had been established on the grounds that the average supernova rate may be high in starbursts as indicated by infrared and radio observations, and at distances of approximately 3 Mpc a significant chance of supernova gamm-ray line detection exists. NGC 253 was detected in continuum emission up to 165 keV with a total significance of 4.4 sigma and an estimated luminosity of 3 x 1040 ergs/s. The spectrum is best fit by a power law of photon index approximately 2.5. We consider the possible contribution of different emission mechanisms, including inverse Compton scattering, bremsstrahlung, discrete sources, and Type Ia/Ib supernova continuum to the measured flux. No significant continuum flux was observed from M82. A search for the gamma-ray line from the decay of the most abundant radioactive element produced in supernovae (Ni-56 yields Co-56 yields Fe-56) yielded no significant detection: the 3 sigma upper limits to the line fluxes at 0.158, 0.812, 0.847, and 1.238 MeV for both galaxies are obtained
