Abstract: The possibility off measuring for the first time neutrino-nuclei coherent scattering has been recently discussed by several experimental collaborations. It is shown that such a measurement may be very sensitive to non-standard interactions of neutrinos with quarks and might set better constraints than those coming from future neutrino factory experiments. We also comment on other types of new physics tests, such as extra heavy neutral gauge bosons, where the sensitivity to some models is slightly better than the Tevatron constraint and, therefore, could give complementary bounds.