[1] Cosmic ray drift directions depend both on the charge of the particle population under consideration, as well as the heliospheric magnetic field polarity which oscillates within a ∼22 year cycle. The differences in the cosmic ray drift patterns between successive solar cycles manifest themselves in the sign of the latitudinal cosmic ray gradient. For positively charged particles, a positive latitudinal gradient is expected in the qA > 0 polarity cycle, while a negative value is expected in the qA < 0 cycle. For the first time observed radial and latitudinal values for anomalous cosmic ray oxygen are available in both of these cycles. In the present qA < 0 cycle, the observations seem, however, inconsistent with the drift-dominated considerations discussed above, as the latitudinal gradient is smaller than expected and perhaps even positive. This issue is addressed by using a comprehensive numerical model for anomalous cosmic ray acceleration and transport, based on new diffusion coefficients, to simulate these gradients over the previous two magnetic polarity cycles. Computed gradients and energy spectra (at Earth and at Ulysses) are compared to observations, with good agreement achieved between observations and model predictions. For the qA > 0 cycle, the model predicts a positive latitudinal gradient but for the qA < 0 cycle a latitudinal gradient that is smaller and that can be either positive or negative. It is concluded that drifts and poleward diffusion set up competing latitudinal gradients in the qA < 0 cycle, with the resulting sign of the gradient determined by the most effective of the two processes.Citation: Strauss, R. D., and M. S. Potgieter (2010), Modeling anomalous cosmic ray oxygen gradients over successive solar cycles,