  In the presence of a strong magnetic field a stellar equilibrium
configuration, aided by the Lorentz force, can support a larger mass than a
non-magnetic one. This has been considered a possible explanation of the
super-Chandrasekhar mass white dwarfs giving rise to over-luminous Type-Ia
supernovae. We present here linear and non-linear perturbation studies of such
strongly magetised configurations and show that axisymmetric configurations
with poloidal or toroidal fields are unstable. The numerical evolution of the
perturbations shows instability after about an Alfv\'en crossing time. This
time scale is very short for the magnetically supported super-Chandrasekhar
mass white dwarfs. Uniform rotation about the symmetry axis can reduce the
growth rate but can not stabilize the super-massive configurations. It is
concluded that long-lived super-Chandrasekhar mass white dwarfs supported by
magnetic field are unlikely to occur in Nature.
