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It is shown that the future SNO and Super-Kamiokande experiments, in whichhigh energy $^8\mathrm{B}$ neutrinos will be detected through the observationof CC, NC and $\nu$--$e$ elastic scattering processes, could allow to reveal ina model independent way the presence of sterile neutrinos in the flux of solarneutrinos on the earth. Lower bounds for different averaged values of theprobability of transition of solar $\nu_e$'s into sterile states and for thetotal flux of $^8\mathrm{B}$ neutrinos are derived in terms of measurablequantities. 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 thecase 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 aregiven.Comment: 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.

Are there sterile neutrinos in the flux of solar neutrinos on the earth?