  It is shown that the future SNO and Super-Kamiokande experiments, in which
high energy $^8\mathrm{B}$ neutrinos will be detected through the observation
of CC, NC and $\nu$--$e$ elastic scattering processes, could allow to reveal in
a model independent way the presence of sterile neutrinos in the flux of solar
neutrinos on the earth. Lower bounds for different averaged values of the
probability of transition of solar $\nu_e$'s into sterile states and for the
total flux of $^8\mathrm{B}$ neutrinos are derived in terms of measurable
quantities. The possibilities to reveal the presence of $\nu_\mu$ and/or
$\nu_\tau$ in the solar neutrino flux on the earth are also considered and the
case of transitions of solar $\nu_e$'s only into sterile states is discussed.
Some numerical results for a simple model with $\nu_e$--$\nu_s$ mixing are
given.
