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

General description of spin motion in storage rings in presence of oscillating horizontal fields