  We study the relation of optical/UV and X-ray emission in the low luminosity
active galactic nuclei (LLAGNs), using a sample of 49 sources including 28
local Seyfert galaxies and 21 low-ionization nuclear emission-line regions
(LINERs) with the optical/UV spectral luminosity at the wavelength
\lambda=2500\AA, 23.0\leq \log L_{\nu(2500\AA)(erg/s/Hz)\leq 27.7, and the
X-ray spectral luminosity at 2 keV, 20.5\leq \log L_{\nu(2 keV)}\leq 25.3. The
strong correlations are found between the X-ray luminosity and the optical/UV
to X-ray index, \alpha_{ox}, with the optical/UV luminosity, with the slopes
very similar to the findings for the luminous AGNs in the previous works. The
correlation between \alpha_{ox} and L_{\nu(2 keV) is very weak as that found
for the luminous AGNs in the majority of previous similar works. We also study
the relation between $\alpha_{\rm ox} and the Eddington ratio L_{bol}/L_{Edd}
for our sample and find a significant anti-correlation for the sources with
L_{bol}/L_{Edd}\lesssim 10^{-3}, which is opposite to the correlation between
the two variables for the luminous AGNs. Using the advection dominated
accretion flow (ADAF) model, we roughly reproduce this anti-correlationship for
the two variables for the LLAGNs. This result strongly supports the ADAF as a
candidate accretion mode in LLAGNs.
