The two nearby starburst galaxies M82 and NGC 253 were observed for \sim 100 ksec over a 10-month period in 1997 . An increase of the M82 flux by a factor \sim 2 was measured during the period July-November , when compared with the flux measured earlier in 1997 . The flux measured in the field centered on M82 includes \sim 38 \% of the emission from the Seyfert 1 galaxy M81 . The best-fitting model for the earlier emission from M82 is thermal with kT \simeq 6.7 \pm 0.1 keV . In the high flux state , the emission additionally includes either an absorbed second thermal component or absorbed power-law component , with the former providing a much better fit . A likely origin for the temporal variability is a single source in M82 . The flux of NGC 253 , which did not vary significantly during the period of observations , can be well fit by either a thermal spectrum with kT \simeq 3.8 \pm 0.3 keV , or by a power law with photon index of 2.7 \pm 0.10 . We have also attempted fitting the measurements to more realistic composite models with thermal and power-law components , such as would be expected from a dominant contribution from binary systems , or Compton scattering of ( far ) IR radiation by radio emitting electrons . However , the addition of any amount of a power-law component , even with cutoff at 20 keV , only increases chi-square . The 90 % confidence upper limit for power law emission with ( photon ) index 1.5 is only 2.4 % of the 2 — 10 keV flux of M82 ; the corresponding limit for NGC 253 , with index 2.0 , is 48 % .