  The renormalization group evolution equation for two neutrino mixing is known
to exhibit nontrivial fixed point structure corresponding to maximal mixing at
the weak scale. The presence of the fixed point provides a natural explanation
of the observed maximal mixing of $\nu_{\mu}-\nu_{\tau}$ if the $\nu_{\mu}$ and
$\nu_{\tau}$ are assumed to be quasi-degenerate at the seesaw scale without
constraining on the mixing angles at that scale. In particular, it allows them
to be similar to the quark mixings as in generic grand unified theories. We
discuss implementation of this program in the case of MSSM and find that the
predicted mixing remains stable and close to its maximal value, for all
energies below the $O$(TeV) SUSY scale. We also discuss how a particular
realization of this idea can be tested in neutrinoless double beta decay
experiments.
