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 $��$--$e$ 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 $��_e$'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 $��_��$ and/or $��_��$ in the solar neutrino flux on the earth are also considered and the case of transitions of solar $��_e$'s only into sterile states is discussed. Some numerical results for a simple model with $��_e$--$��_s$ mixing are given.

Revised reference list. Revtex file, 15 pages + 4 figures (included). The postscript file of text and figures is available at ftp://toxd01.to.infn.it/pub/giunti/1995/dftt-12-95/dftt-12-95.ps.Z