Large nu(mu)->nu(tau) and nu(e)->nu(tau) transitions in short-baseline experiments?

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.