  If active to active neutrino transitions are dominant modes of the
atmospheric ($\nu_{\mu} \to \nu_{\tau}$) and the solar neutrino oscillations
($\nu_{e}\to \nu_{\mu}/\nu_{\tau}$), as is indicated by recent data, the
favoured scheme which accommodates the LSND result - the so called (2+2)-scheme
- should be discarded. We introduce the parameters $\eta_s^{atm}$ and
$\eta_s^{sun}$ which quantify an involvement of the sterile component in the
solar and atmospheric neutrino oscillations. The (2+2)-scheme predicts
$\eta_s^{atm} + \eta_s^{sun} = 1$ and the experimental proof of deviation from
this equality will discriminate the scheme. In this connection the (3+1)-scheme
is revisited in which the fourth (predominantly sterile) neutrino is isolated
from a block of three flavour neutrinos by the mass gap $\Delta m^2_{LSND} \sim
(0.4-10)$ eV$^2$. We find that in the (3+1)-scheme the LSND result can be
reconciled with existing bounds on $\nu_e$- and $\nu_{\mu}$ - disappearance at
95-99 % C.L.. The generic prediction of the scheme is the $\nu_e$- and
$\nu_{\mu}$ - disappearance probabilities at the level of present experimental
bounds. The possibility to strengthen the bound on $\nu_{\mu}$- disappearance
in the KEK - front detector experiment is studied. We consider phenomenology of
the (3 + 1)-scheme, in particular, its implications for the atmospheric
neutrinos, neutrinoless double beta decay searches, supernova neutrinos and
primordial nucleosynthesis.
