Spectral fits to X-ray data from both NGC 253 and M82 provide ambiguous res
ults. The so-called best-fit results depend on the instrument with which th
e data were obtained and, obviously, on the choice of spectral model compos
ition. We show that different spectral models can be fit equally well to Be
ppoSAX data of both galaxies. Metallicities are unreliable in general, with
a strong dependence on the choice of model. Preference to one particular s
pectral model can be given only by combining spectroscopic and imaging X-ra
y data from all available satellites (ROSAT, ASCA, and BeppoSAX). Based on
spectra of NGC 253, we demonstrate that a model consisting of two or more t
hermal plasma components plus a hard power-law continuum and Fe Ka line emi
ssion can explain all observations. These model components represent the in
tegral spectrum of thermal gas and compact sources in starburst galaxies th
at are most likely supernova remnants and X-ray binaries. The same model ca
n fit the X-ray data of M82, but there the evidence, from ROSAT imaging, of
the existence of compact sources which might represent high-mass X-ray bin
aries is weaker. This implies that its hard X-ray emission, which is extend
ed in ROSAT images, might-if truly diffuse-be dominated by a very hot (seve
ral keV energy) thermal gas component.