  We discuss the issues of stability of accretion disks that may undergo the
limit-cycle oscillations due to the two main types of thermal-viscous
instabilities. These are induced either by the domination of radiation pressure
in the innermost regions close to the central black hole, or by the partial
ionization of hydrogen in the zone of appropriate temperatures. These physical
processes may lead to the intermittent activity in AGN on timescales between
hundreds and millions of years. We list a number of observational facts that
support the idea of the cyclic activity in high accretion rate sources. We
conclude however that the observed features of quasars may provide only
indirect signatures of the underlying instabilities. Also, the support from the
sources with stellar mass black holes, whose variability timescales are
observationally feasible, is limited to a few cases of the microquasars.
Therefore we consider a number of plausible mechanisms of stabilization of the
limit cycle oscillations in high accretion rate accretion disks. The newly
found is the stabilizing effect of the stochastic viscosity fluctuations.
