Experimental results on the elastic scattering of reactor neutrinos off ele
ctrons are analyzed in order to find the contribution from the neutrino mag
netic moment to the elastic scattering cross section. The potentials of sea
rching for the magnetic moment in accelerator and reactor experiments are c
ompared with each other. An upper limit on the possible neutrino magnetic m
oment is found to be mu (v) less than or equal to 1.5 x 10(-10) mu (B) (90%
C.L.). The possibility of improving the sensitivity of the reactor experim
ents up to a level of 10(-11) mu (B) is discussed.