Our 3-D model for the solar cycle (SC) effect on the QBO (H. G. Mayr et al., The QBO as potential amplifier of solar cycle influence, submitted to Geophysical Research Letters, 2005, hereinafter referred to as Mayr et al., submitted manuscript, 2005) produces a hemispherically symmetric 12-month Annual Oscillation (AO) in the zonal winds, which is largely confined to low latitudes. This Equatorial Annual Oscillation (EAO) is generated through nonlinear interaction between the dominant anti-symmetric AO and the anti-symmetric component of the SC response. Due to wave-mean-flow interaction from small-scale gravity waves (GW), the SC-modulated EAO is amplified and propagates down through the stratosphere as does the QBO. The amplitude of the EAO is relatively small, but its SC modulation is large and is in phase with that of the QBO. Although the EAO is concentrated at low latitudes, prominent signatures appear in the polar regions where the SC produces measurable temperature variations. At lower altitudes, the GW-driven downward propagation of the EAO affects the phase of the annual cycle and causes the SC effect to be different in the two hemispheres.