  The general theoretical description of the influence of oscillating
horizontal magnetic and quasimagnetic fields on the spin evolution in storage
rings is presented. Previous results are generalized to the case when both of
the horizontal components of the oscillating field are nonzero and the vector
of this field circumscribes an ellipse. General equations describing a behavior
of all components of the polarization vector are derived and the case of an
arbitrary initial polarization is considered. The derivation is fulfilled in
the case when the oscillation frequency is nonresonant. The general spin
evolution in storage rings conditioned by vertical betatron oscillations is
calculated as an example.
