  BeppoSAX observations of the nearby archetypical starburst galaxies NGC253
and M82 are presented. Spectral analysis shows that the 2-10 keV spectra of
both galaxies, extracted from the central 4' regions, are best fitted by a
thermal emission model with kT~6-9 keV and metal abundances ~ 0.1-0.3 solar.
The spatial analysis yields clear evidence that this emission is extended in
NGC 253, and possibly also in M82. These results clearly rule out a LLAGN as
the {\it main} origin of the X-ray emission in NGC 253. For M82, the presence
of an Fe-K line at ~ 6.7 keV, and the convex profile of its 2-10 keV continuum,
indicate a significant thermal component. Contributions from point sources
(e.g. X-ray binaries, supernova remnants, and/or a LLAGN) and Compton emission
are also likely. Altogether, BeppoSAX results provide compelling evidence for
the existence of a hot interstellar plasma in both galaxies, possibly in the
form of superwind outflows from the disks of these galaxies. Order-of-magnitude
estimates and some implications, such as the expelled mass and the energetics
of the outflowing gas of this superwind scenario, are discussed. These new
results also suggest some similarity between the X-ray emission from these
galaxies and that from the Galactic Ridge.
