Product branching fractions and kinetic isotope effects for the reactions of OH and OD radicals with CH3SH and CH3SD were determined from the infrared chemiluminescent spectra of the H2O, KDO and D2O products. The spectra were acquired by a Fourier transform spectrometer that viewed the emission from a discharge flow reactor. Abstraction of H atom from the methyl group accounts for (11 +/- 4)% of the total reaction rate from the OD + CH3SD (or OD + CH3SH) reaction and for (24 +/- 8)% from the OH + CH3SH (or OH + CH3SD) reaction. The major product channel involves interaction with the sulfur end of the molecule. The difference in branching fractions for OD and OH reactions is due to the large inverse secondary kinetic-isotope effect for the addition-elimination channel, which occurs by transfer of the hydrogen atom from the sulfur atom to the oxygen atom in the adduct. Transition state models for the elimination channel are discussed to show that the experimentally determined secondary kinetic isotope effect for the addition-elimination step, k(OH)/k(OD) = 0.6 +/- 0.1, Obtained from the intensity ratios is reasonable. The basis spectra used for simulation of the Delta v(3) = -1 emission spectra of D2O were refined, relative to previous work, and the improvements are described in the Appendix.