OSSE observed the starburst galaxy M82 in two viewing periods of 8 and 14 days. M82’s priority as a target had been established on the grounds that the average supernova rate may be very high there, so that a significant chance of 56Co detection exists. If M82 is at 3.4 Mpc distance, normal Type II (e.g. SN1987A) are too dim in 56Co lines, but the Wolf‐Rayet derived Type Ib, which are also massive‐star core implosion objects, might be detectable to OSSE. Expected fluxes of the 847 keV γ‐line of 56Co would be near (2–5)×10−5 γ cm−2 s−1. A Type Ia in M82 would be very bright, near (3–6)×10−4 γ cm−2 s−1. We present OSSE background subtracted spectra of the M82 region for viewing periods 7 and 18. These spectra show no significant excess at 847 keV or at 1238 keV, the two strongest 56Co γ‐lines. When we fit a smooth gamma continuum plus a feature having both the 847 keV and 1238 keV lines to the OSSE data, we obtain for the 847 keV line amplitude the values (−4.18±3.45)×10−5 γ cm−2 s−1 for viewing period 7 an...