  We have found compact, near-nuclear X-ray sources in 21 (54\%) of a complete
sample of 39 nearby face-on spiral and elliptical galaxies with available ROSAT
HRI data. ROSAT X-ray luminosities (0.2 $-$ 2.4 keV) of these compact X-ray
sources are $\sim$10$^{37}$$-$10$^{40}$ erg~s$^{-1}$. The mean displacement
between the location of the compact X-ray source and the optical photometric
center of the galaxy is $\sim$390 pc. ASCA spectra of six of the 21 galaxies
show the presence of a hard component with relatively steep ($\Gamma \approx$
2.5) spectral slope. A multicolor disk blackbody plus power-law model fits the
data from the spiral galaxies well, suggesting that the X-ray objects in these
galaxies may be similar to a black hole candidate (BHC) in its soft (high)
state. ASCA data from the elliptical galaxies indicate that hot (kT $\approx$
0.7 keV) gas dominates the emission. The fact that the spectral slope of the
spiral galaxy sources is steeper than in normal type 1 active galactic nuclei
(AGNs) and that relatively low absorbing columns (N$_H \approx$ 10$^{21}$
cm$^{-2}$) were found to the power-law component indicates that these objects
are somehow geometrically and/or physically different from AGNs in normal
active galaxies. The X-ray sources in the spiral galaxies may be BHCs,
low-luminosity AGNs, or possibly X-ray luminous supernovae. We estimate the
black hole masses of the X-ray sources in the spiral galaxies (if they are BHCs
or AGNs) to be $\sim$10$^2$$-$10$^3$ M$_\odot$. The X-ray sources in the
elliptical galaxies may be BHCs, AGNs or young X-ray supernova also.
