The authors present spectroscopic data on the O6 + WN3 binary R31 in the SMC, which improve the orbital determination of Moffat (1982). The period is found to be 6.538 days. From several considerations they consider an eccentricity of ≡0.2 to be possible. From the absence of known eclipses and lack of evidence that the primary fills its Roche lobe, they infer that the orbital inclination is ≡60° or less. The stellar masses are most probably 65 Msun; and 12 Msun;. This makes the O star one of the most massive yet measured. Velocity differences between absorption lines of different ions are thought to be due to stellar wind effects, and may be phase dependent. The unusually large mass ratio is discussed.