  We report the results from a deep ROSAT PSPC observation of LINER galaxy NGC
4736. Two bright sources are detected, separated by only about 1', with the
brighter one coinciding with the center of the galaxy. Neither source shows
apparent X-ray variability on time-scales of minutes to hours in the ROSAT
band. Simple power-law models, typical of AGN X-ray spectra, produce poor fits
to the observed X-ray spectrum of the nuclear source. The addition of a
Raymond-Smith component improves the fits significantly. This is consistent
with the presence of hot gas in the nuclear region with kT=~0.3 keV, in
addition to a compact nuclear source. However, a careful examination of the
residuals reveal apparent features at low energies (< 0.25 keV). We find that
the addition of a narrow emission line at about 0.22 keV is a significant
improvement to the parameterization of the spectrum. We examine the results in
the light of the accuracy of the PSPC spectral calibration. The derived photon
index is about 2.3, which is similar to those for Seyfert 1 galaxies measured
in the ROSAT energy range. On the other hand, the 0.1-2 keV luminosity for the
compact source is only about 3.4x10^{39} erg/s, much fainter than typical
Seyfert galaxies. We discuss the implications of these results on the
connection between LINERs and AGNs.
  The off-center source is transient in nature. It has a hard X-ray spectrum,
with a photon index of about 1.5, so is likely to be an X-ray binary. There is
still some ambiguity regarding its association with the galaxy. If it is indeed
located in the galaxy, the 0.1-2 keV luminosity would be greater than
5.1x10^{38} erg/s, making it a stellar-mass black hole candidate.
