The reaction between dimethyl ether radicals and molecular oxygen proceeds along two distinct pathways at temperatures between 230 and 350 K. Above about 100 Torr total pressure the peroxy radical, CH3OCH2O2, is predominantly formed. As the pressure is reduced, a channel leading to the formation of OH and two formaldehyde molecules becomes progressively more important. Real time kinetic measurements of these reactions are made using time-resolved UV spectroscopy to monitor CH3OCH2 loss and CH3OCH2O2 formation along with transient IR absorption to probe formaldehyde production. The OH radicals are identified via their UV spectrum. The reaction can be described via a modified Lindemann mechanism using the three parameters k(ro2 infinity), k(ro2,0), and k(prod,0), which represent the high- and low-pressure limits of the O-2 addition reaction and the low-pressure limit of the OH/formaldehyde channel. At 295 K they have values of (1.1 +/- 0.1) x 10(-11) cm(3) s(-1), (2.6 +/- 0.9) x 10(-29) cm(6) s(-1), and (6 +/- 2) x 10(-12) cm(3) s(-1), respectively. At P-tot = similar to 120 Torr the reaction exhibits a negative temperature dependence with k(r+o2) = (3.1(-0.8)(+1.0)) x 10(-12) e((326+/-80)/T) cm(3) s(-1). Experiments in the absence of oxygen were performed to investigate the CH3OCH2-mediated chain reaction between chlorine and dimethyl ether. Analysis of time-resolved UV spectra reveals rate constants of k(r+cl2) = (1.8(-0.5) (+0.7)) x 10(-11) e((360+/-120)/T) cm(3)s(-1) and k(r+r) = (1.8(-0.5)(+0.6)) x 10(-11) e((200+/-100)/T) cm(3)s(-1), respectively, for the chain propagation reaction between CH3OCH2 and molecular chlorine and for the chain-terminating recombination reaction.