The reflected shock tube technique with multipass absorption spectrometric detection of OH radicals at 308 nm has been used to study the reactions OH + CH4 --> CH3 + H2O and CH3 + NO2 --> CH3O + NO. Over the temperature range 840-2025 K, the rate constants for the first reaction can be represented by the Arrhenius expression k = (9.52 +/-1.62) x 10(-11) exp[(-4134 +/- 222 K)/T] cm(3) molecule(-1) s(-1). Since this reaction is important in both combustion and atmospheric chemistry, there have been many prior investigations with a variety of techniques. The present results extend the temperature range by 500 K and have been combined with the most accurate earlier studies to derive an evaluation over the extended temperature range 195 - 2025 K. A three-parameter expression describes the rate behavior over this temperature range, k = (1.66 x 10(-18))T-2.182 exp[(-1231 K)/T] cm(3) molecule(-1) s(-1). Previous theoretical studies are discussed, and the present evaluation is compared to earlier theoretical estimates. Since CH3 radicals are a product of the reaction and could cause secondary perturbations in rate constant determinations, the second reaction was studied by OH radical production from the fast reactions CH3O --> CH2O + H and H + NO2 --> OH + NO. The measured rate constant is 2.26 x 10(-11) cm(3) molecule(-1) s(-1) and is not dependent on temperature from 233 to 1700 K within experimental error.