Due to a host of experimental and chemical complications, there has been extremely high variability in the literature results for the kinetics of the H atom abstraction reaction between OH and CH3SCH3 (DMS). In particular, as a result of a wall reaction between OH and DMS, this reaction stands as the prime example of one which severely restricts the capability of the low-pressure discharge flow technique to measure gas-phase, homogeneous rate constants. In this study, the "wall-less" high-pressure discharge flow technique is used to measure the kinetics for this reaction, and for the related reaction between OH and CH3SSCH3 (DMDS), over the temperature range from 297 to 368 K. To the 95% confidence level, the results are as follows: for OH/CH3SCH3, (1.35 +/- 0.62) x 10(-11)e(-285 +/- 135)/T and (4.98 +/- 0.46) x 10(-12) at 297 K, and for OH/CH3SSCH3, (6.2 +/- 4.9) x 10(-11)e(410 +/- 210)/T and (2.39 +/- 0.30) x 10(-10) at 297 K, where the units are cm3 molecule-1 S-1. The results for the OH/DMS reaction are similar to those of specific studies performed with the complementary flash photolysis technique. The agreement between two dissimilar approaches increases our confidence in the literature database for this reaction. The mechanisms of these reactions are discussed in terms of orbital interactions.