  It is argued that the observed deficit of solar and atmospheric neutrinos can
be explained by neutrino oscillations $\nu_e \to \nu_s $ and $\nu_\mu \to
\nu'_{s}$ involving two hypothetic sterile neutrinos $\nu_s $ and $\nu'_{s} $
(blind to all 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.
