The theory of depolarization in circular accelerators is presented. The spin equation is first expressed in terms of the particle orbit and then converted to the equivalent spinor equation. The spinor equation is then solved for three different situations: (1) a beam on a flat top near a resonance, (2) uniform acceleration through an isolated resonance, and (3) a model of a fast resonance jump. Finally, the depolarization coefficient, epsilon, is calculated in terms of properties of the particle orbit and the results are applied to a calculation of depolarization in the AGS.