  We suggest the possibility that the anomalies observed in the LSND experiment
and the Gallium radioactive source experiments may be due to neutrino
oscillations generated by a large squared-mass difference of about 20 - 30
eV^2. We consider the simplest 3+1 four-neutrino scheme that can accommodate
also the observed solar and atmospheric neutrino oscillations. We show that, in
this framework, the disappearance of nu_e and nu_mu in short-baseline neutrino
oscillation experiments is mainly due to active-sterile transitions. The
implications of the first MiniBooNE results, appeared after the completion of
this paper, are discussed in an addendum.
