[en] If neutrinos have non-vanishing mass and non-vanishing magnetic moments, then electron neutrinos emitted in nuclear reactions in the solar interior may undergo flavour oscillations, spin precession or resonant spin-flavour precession. Assuming equal values for the magnetic moments of all neutrino flavours and using the data from Homestake and SuperKamiokande we obtain an upper limit on the neutrino magnetic moment and find μ_νe ≤ (2.2-2.3) x 10^-10 μ_B, within four standard solar models. We also point out that this limit may be further reduced if the detector threshold energy for the ν_e,xe^- scattering is decreased