  Considering four-neutrino schemes of type 3+1, we identify four small regions
of the neutrino mixing parameter space compatible with all data. Assuming a
small mixing between the sterile neutrino and the isolated mass eigenstate we
show that large nu_mu->nu_tau and nu_e->nu_tau transitions are predicted in
short-baseline experiments and could be observed in the near future in
dedicated experiments. We discuss also implications for solar, atmospheric and
long-baseline neutrino experiments and we present a formalism that allows to
describe in 3+1 schemes atmospheric neutrino oscillations, long-baseline nu_mu
disappearance and nu_mu->nu_tau transitions in matter.
