  The results of a 0.4-10.0 keV ASCA spectral analysis of a sample of
low-luminosity AGN (LLAGN; M51, NGC 3147, NGC 4258), low-ionization nuclear
emission line regions (LINERs; NGC 3079, NGC 3310, NGC 3998, NGC 4579, NGC
4594) and starburst galaxies (M82, NGC 253, NGC 3628 and NGC 6946) are
presented. In spite of the heterogeneous optical classifications of these
galaxies, the X-ray spectra are fit well by a ``canonical'' model consisting of
an optically-thin Raymond-Smith plasma ``soft'' component with T ~ 7 x 10^6 K
and a ``hard'' component that can be modeled by either a power-law with a
photon index ~ 1.7 or a thermal bremsstrahlung with T ~ 6 x 10^7 K. The
soft-component 0.4-10 keV instrinsic luminosities tend to be on the order
10^39-40 ergs/s while the hard-component luminosities tend to be on the order
of 10^40-41 ergs/s. The detection of line emission is discussed. An analysis of
the short-term variability properties was given in Ptak et al. (1998) and
detailed interpretation of these results will be given in Paper II. (abridged)
