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 similar to 6-9 keV and metal abundances 0.1
-0.3 solar. The spatial analysis yields clear evidence that this emission i
s extended in NGC 253, and possibly also in M82. These results clearly rule
out a LLAGN as the main origin of the X-ray emission in NGC 253. For M82,
the presence of an Fe-K line at similar to 6.7 keV, and the convex profile
of its 2-10 keV continuum, indicate a significant thermal component. Contri
butions from point sources (e.g. X-ray binaries, supernova remnants, and/or
a LLAGN) and Compton emission are also likely. Altogether, BeppoSAX result
s provide compelling evidence for the existence of a hot interstellar plasm
a in both galaxies, possibly in the form of superwind outflows from the dis
ks of these galaxies. Order-of-magnitude estimates and some implications, s
uch as the expelled mass and the energetics of the outflowing gas of this s
uperwind scenario, are discussed. These new results also suggest some simil
arity between the X-ray emission from these galaxies and that from the Gala
ctic Ridge.