If active to active neutrino transitions are dominant modes of the atmospheric (ν µ → ν τ ) and the solar neutrino oscillations (ν e → ν µ /ν τ ), 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 η atm s and η sun s which quantify an involvement of the sterile component in the solar and atmospheric neutrino oscillations. The (2+2)-scheme predicts η atm s +η sun s= 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 ∆m 2 LSN D ∼ (0.4 − 10) eV 2 . We find that in the (3 + 1)-scheme the LSND result can be reconciled with existing bounds on ν e -and ν µ -disappearance at 95−99% C.L.. The generic prediction of the scheme is the ν e -and ν µ -disappearance probabilities at the level of present experimental bounds.The possibility to strengthen the bound on ν µ -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.