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The results of a 0.4-10.0 keV ASCA spectral analysis of a sample oflow-luminosity AGN (LLAGN; M51, NGC 3147, NGC 4258), low-ionization nuclearemission line regions (LINERs; NGC 3079, NGC 3310, NGC 3998, NGC 4579, NGC4594) and starburst galaxies (M82, NGC 253, NGC 3628 and NGC 6946) arepresented. In spite of the heterogeneous optical classifications of thesegalaxies, the X-ray spectra are fit well by a ``canonical'' model consisting ofan optically-thin Raymond-Smith plasma ``soft'' component with T ~ 7 x 10^6 Kand a ``hard'' component that can be modeled by either a power-law with aphoton index ~ 1.7 or a thermal bremsstrahlung with T ~ 6 x 10^7 K. Thesoft-component 0.4-10 keV instrinsic luminosities tend to be on the order10^39-40 ergs/s while the hard-component luminosities tend to be on the orderof 10^40-41 ergs/s. The detection of line emission is discussed. An analysis ofthe short-term variability properties was given in Ptak et al. (1998) anddetailed interpretation of these results will be given in Paper II. (abridged)Comment: Accepted for Jan. 99 issue of ApJS. 35 pages with embedded postscript  figures. 8 large tables included externally as postscript file

X‐Ray Constraints on Accretion and Starburst Processes in Galactic Nuclei. I. Spectral Results