A combined flash photolysis/shock-tube technique for the direct investigation of the rates of bimol. reactions of the OH radical at temps. between 1000-1500 K is described. In this technique shock heated mixts. of approx. 0.5% of H2O in Ar and contg. small amts. of a selected reactant are subjected to flash photolysis as an instantaneous source of OH. The shock wave only serves to heat the gas mixt.; thermal decompn. does not occur. Formation and subsequent decay of OH are monitored by time resolved UV resonance absorption. First results with this technique were obtained for the reactions (1) OH + CH4 -> CH3 + H2O and (2) OH + CF3H -> CF3 + H2O. Rate consts. were k1 (1300 K) = (2.5 +- 0.8)*1012 and k2 (1350 K) = (4.0 +- 1.0)*1011 cm3 mols. The result of reaction (1) is shown to confirm previously suggested non-Arrhenius behavior for this reaction, and in combination with low temp. data yields k1(T) = 106.19 (T/K)2.13 exp(-1234 K/T)cm3 mols. The dependence of k1 on temp. is described in terms of transition state theory.