Numerical calculations of fluid dynamos are used to constrain the probable origin of toroidal flows in the outer core. Azimuthal drift of the core fluid relative to the mantle is the sum of three components: (1) uniform differential rotation of the core relative to the mantle produced by electromagnetic torques on the mantle; (2) cylindrical flow driven by electromagnetic torques in the core, and (3) buoyantly driven thermal wind flow produced by lateral variations of temperature and composition. Dynamo calculations indicate that electromagnetic torques on the mantle contribute to long-term drift, but are not likely to be its primary cause. Zonal flow driven by electromagnetic torques in the core and thermal wind flows driven by zonal temperature gradients are both sufficiently energetic to account for azimuthal flows with angular velocities of 0.1--0.5¿ yr-1, as inferred from frozen flux analyses of secular variation. ¿ American Geophysical Union 1989