It is argued that the observed deficit of solar and atmospheric neutrinos c
an be explained by neutrino oscillations nu(e) --> nu(s) and nu(mu) --> nu(
s)' involving two hypothetic sterile neutrinos nu(s) and nu(s)' (blind to a
ll Standard-Model interactions). They are keen to mix nearly maximally with
nu(e) and nu(mu), respectively, to form neutrino mass states nu(1), nu(4)
and nu(2), nu(5). Our argument is presented in the framework of a model of
fermion "texture" formulated previously, which implies the existence of two
sterile neutrinos beside the three conventional.