We measured the first high-temperature rate measurements of two dimethyl ether (DME) reactions, (1) DME + Ar -> CH3O + CH3 + Ar and (2) DME + OH -> CH3OCH2 + H2O, in a shock tube by monitoring OH radicals. OH was measured with a narrow-line width laser absorption diagnostic using the well-known R-1(5) line of the A-X(0,0) transition at 306.7 nm. The rate k(1) is in the falloff regime at high temperatures, so it was measured at several pressures from 0.6 to 11.5 atm and temperatures from 1349 to 1790 K. OH radicals were formed by shock-heating mixtures of DME and O-2 in Ar. These mixtures take advantage of the rapid decomposition of the product CH3O, forming H-atoms, which react with O-2 to form OH. In carefully chosen mixtures, OH concentration is primarily sensitive to k(1) and the well-known rate of H + O-2 -> OH + O. Uncertainty in the k(1) measurements was estimated to be +/- 35%. The rate measurements were then modeled using RRKM theory, which describes the data quite well. Both the rate measurements and the RRKM model were fit from 1000 to 1800 K using the Troe falloff form: k(1,infinity)(T) = (4.38 x 10(21))T-1.57 exp(-42 220 K/T) s(-1), k(1.0) = 7.52 x 10(15) exp(-21 537 K/T) cm(3) mol(-1) s(-1), and F-cent = 0.454 exp(-T/2510). The rate of k(2) was measured at pressures near 1.6 atm and temperatures from 923 to 1423 K. OH radicals were generated by the thermal decomposition of the OH precursor tert-butyl hydroperoxide (TBHP), and k(2) Was inferred from the observed decay of OH with all estimated uncertainty of 40%. The high-temperature measurements were compared with several rate evaluations and previous low-temperature measurements. The rate evaluation by Curran et al. of k(2) = (6.32 x 10(6))T-2 exp(328 K/T) (cm(3) mol(-1) s(-1)) was found to be all excellent fit to both the previous low-temperature measurements and this work.