We analyzed six low-luminosity active galactic nuclei (hereafter LLAGNs), w
hich consist of two bright LINERS (low-ionization nuclear emission line reg
ion) with broad Hoe, and of four bright low-luminosity Seyferts observed by
the X-ray satellite ASCA. We examined the time variabilities of these targ
ets, and found that most targets show no significant time variabilities, al
though these galaxies belong to LLAGNs. By applying Fourier analysis to the
ir light curves in the 2-10 keV band, we obtained the lower limits of their
time variability scales, which correspond to their central black hole mass
es greater than several times 10(6) M-circle dot. Our result suggests that
these LLAGNs are harbors of super-massive black holes. but the emitting pow
ers are only < 1% of the Eddington luminosities of the central engines in t
he LLAGNs due to their small accretion rates. Since a black hole would grow
by mass accretion, it is hard to create Such a super-massive black hole un
der a small accretion rate. Therefore, the mass-accretion rates in the past
must have been larger than those at present, and the galaxies have probabl
y been as luminous as QSOs. This will be a hint to find out the cause of th
e lack of QSOs in the local universe.