The influence of an external electric field on the spin dynamics of an elec
trically neutral Fermi liquid is considered, the mechanism of such an influ
ence being the relativistic spin-orbital interaction. As a result, Leggett
's equations for the spin dynamics of weakly polarized Fermi liquids are ge
neralised to the case of non-zero external electric field. In addition, we
obtained the transverse spin dynamics equation for strongly spin-polarized
liquids in an electric field at zero temperature. In both situations covari
ant derivatives depending on the electric field are shown to be substituted
for spatial gradients in line with the SU(2) gauge invariance of the micro
scopic Hamliltonian. The new equations are applied to the study of spin flo
w along a channel, where an electric field is found to bring about an addit
ional phase shift of thc order of magnitude of the phase shift in superflui
d He-3 -B but growing with time.