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This work supplements the Earth Observing System (EOS) Microwave Limb Sounder (MLS) clear-sky unpolarized forward model with algorithms for modeling polarized emission from the Zeeman-split 118.75-GHz O2 spectral line. The model accounts for polarization-dependent emission and for correlation between polarizations with complex, 2×2 intensity and absorption matrices. The oxygen line is split into three Zeeman components by the interaction of oxygen's electronic spin with an external magnetic field, and the splitting is of order ±0.5 MHz in a typical geomagnetic field. Zeeman splitting is only significant at pressures low enough that collisional broadening (∼1.6 MHz/hPa) is not very large by comparison. The polarized forward model becomes significant for MLS temperature retrievals at pressure below 1.0 hPa and is crucial at pressures below ∼0.03 hPa. Interaction of the O2 molecule with the radiation field depends upon the relative orientation of the radiation polarization mode and the geomagnetic field direction. The model provides both limb radiances and the derivatives of these radiances with respect to atmospheric temperature and composition, as required by MLS temperature retrievals. EOS MLS views the atmospheric limb at 118.75 GHz with a pair of linear-cross-polarized, 100-kHz-resolution, 10-MHz-wide spectrometers. The antennas of the associated receivers are scanned to view rays with tangent heights from the Earth's surface to 0.001 hPa. Comparisons of the modeled MLS radiances with measurements show generally good agreement in line positions and strengths, however residuals in the line centers at the highest tangent heights are larger than desired and still under investigation.