  Zee model leads naturally to two heavy, strongly degenerate and almost
maximally mixed neutrinos and to one light neutrino with small mixing. This
pattern coincides with the one needed for a solution of the atmospheric
neutrino problem by $\n_\m\A \n_\tau$ oscillations and for existence of the two
component hot dark matter in the Universe. Furthermore, the oscillations
$\bar\n_\m\A \bar\n_e$ can be in the range of sensitivity of KARMEN, LSND
experiments. Phenomenology of this scenario is considered and possibility to
check it in the forthcoming experiments is discussed. Scenario implies large
values and inverse flavour hierarchy of the couplings of the Zee boson with
fermions: $f_{e \tau} \ll f_{\mu \tau} \leq f_{e \mu} \sim 0.1$. Main
signatures of scenario are: strongly suppressed signal of $\n_\m\A \n_\tau$
oscillation in CHORUS and NOMAD experiments, so that positive result from these
experiments will rule out the scenario; possibility of observation of $\n_e\A
\n_\tau$ oscillations by CHORUS and NOMAD; corrections to the muon decay,
neutrino-electron scattering at the level of the experimental errors; branching
ratio $B(\mu \A e \gamma)$ bigger than $10^{-13}$. The solar neutrino problem
can be solved by introduction of additional very light singlet fermion without
appreciable changes of the active neutrino pattern.
