  If the generating mechanism for neutrino mass is to account for both the
newly observed muon anomalous magnetic moment as well as the present
experimental bounds on lepton flavor nonconservation, then the neutrino mass
matrix should be almost degenerate and the underlying physics be observable at
future colliders. We illustrate this assertion in two specific examples, and
show that $\Gamma (\mu \to e \gamma)/m_\mu^5$, $\Gamma (\tau \to e
\gamma)/m_\tau^5$, and $\Gamma (\tau \to \mu \gamma) /m_\tau^5$ are in the
ratio $(\Delta m^2)_{sol}^2/2$, $(\Delta m^2)_{sol}^2 /2$, and $(\Delta
m^2)_{atm}^2$ respectively, where the $\Delta m^2$ parameters are those of
solar and atmospheric neutrino oscillations and bimaximal mixing has been
assumed.
