The rate constant for the reaction of CH₃OCH₂ radicals with O₂ (reaction (1)) and the self reaction of CH₃OCH₂ radicals (reaction (5)) were measured using pulse radiolysis coupled with time resolved UV absorption spectroscopy. k₁ was studied at 296 K over the pressure range 0.025-1 bar and in the temperature range 296-473 K at 18 bar total pressure. Reaction (1) is known to proceed through the following mechanism: CH₃OCH₂ + O₂ ↔ CH₃OCH₂O₂^# → CH₂OCH₂O₂H^# → 2HCHO + OH (k_prod) CH₃OCH₂ + O₂ ↔ CH₃OCH₂O₂^# + M → CH₃OCH₂O₂ + M (k_RO2) k₁ = k_RO2 + k_prod, where k_RO2 is the rate constant for peroxy radical production and k_prod is the rate constant for formaldehyde production. The k₁ values obtained at 296 K together with the available literature values for k₁ determined at low pressures were fitted using a modified Lindemann mechanism and the following parameters were obtained: k_RO2,0 = (9.4 ± 4.2) × 10^-30 cm⁶ molecule^-2 s^-1, k_RO2,∞ = (1.14 ± 0.04) × 10^-11 cm³ molecule^-1 s^-1, and kprodi,0 = (6.0 ± 0.5) × 10^-12 cm³ molecule^-1 s^-1 where k_RO2,0 and k_RO2,∞ are the overall termolecular and bimolecular rate constants for formation of CH₃OCH₂O₂ radicals and k_prod,0 represents the bimolecular rate constant for the reaction of CH₃OCH₂ radicals with O₂ to yield formaldehyde in the limit of low pressure. k_RO2,∞ = (1.07 ± 0.08) × 10^-11 exp(-(46 ± 27)/T) cm³ molecule^-1 s^-1 was determined at 18 bar total pressure over the temperature range 296-473 K. At 1 bar total pressure and 296 K, k₃ = (4.1 ± 0.5) × 10^-11 cm³ molecule^-1 s^-1 and at 18 bar total pressure over the temperature range 296-523 K, k₅ = (4.7 ± 0.6) × 10^-11 cm³ molecule^-1 s^-1. As a part of this study the decay rate of CH₃OCH₂ radicals was used to study the thermal decomposition of CH₃OCH₂ radicals in the temperature range 573-666 K at 18 bar total pressure. The observed decay rates of CH₃OCH₂ radicals were consistent with the literature value of k₂ = 1.6 × 10¹³exp(-12800/T) s^-1. The results are discussed in the context of dimethyl ether as an alternative diesel fuel.