Recent experiments using polarized electron beams have shown that spin exchange effects for elastic collisions with ${\mathrm{O}}_2$ and NO are much smaller than for Na atoms. We report calculated spin-flip differential cross sections for elastic collisions of polarized electrons with ${\mathrm{O}}_2$ in agreement with experiment. In general, we can attribute the large variation of the spin-flip differential cross sections to resonances and interference effects. Such features arising from interference, however, may be washed out in the molecular case due to the average over orientations. Calculations with oriented ${\mathrm{O}}_2$ molecules show strong exchange effects as for Na.

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