  Conditions of Velikhov-Chandrasekhar magneto-rotational instability in ideal
and non-ideal plasmas are examined. Linear WKB analysis of hydromagnetic
axially symmetric flows shows that in the Rayleigh-unstable hydrodynamic case
where the angular momentum decreases with radius, the MRI branch becomes
stable, and the magnetic field suppresses the Rayleigh instability at small
wavelengths. We investigate the limiting transition from hydromagnetic flows to
hydrodynamic flows. The Rayleigh mode smoothly transits to the hydrodynamic
case, while the Velikhov-Chandrasekhar MRI mode completely disappears without
the magnetic field. The effects of viscosity and magnetic diffusivity in plasma
on the MRI conditions in thin accretion discs are studied. We find the limits
on the mean free-path of ions allowing MRI to operate in such discs.
