The reflected shock tube technique with a novel multipass absorption spectrometric detection method has been used to study two OH-radical reactions: OH + H-2 --> H2O + H(1), and OH + C2H6 --> H2O + C2H5 (2). Reaction 1 was chosen in order to test the method against earlier rate constant determinations. The measurements on both reactions were performed in single-shot experiments with low initial concentrations of hydroxyl radicals, [OH](0) = (5-15) x 10(12) molecule cm(-3), which allowed reliable isolation of the elementary reactions. The measured rate constants are: k(1) = 5.44 x 10(-11) exp(-3220 K/T) (832-1359 K), and k(2) = 1.10 x 10(-10) exp(-2537 K/T) (822-1367 K), both in cm(3) molecule(-1) s(-1). The present study extends the experimental T-range for reaction 2. This new work and earlier lower-T studies have been combined to give a new evaluation, k(2) = 2.68 x 10(-18) (T/K)(2.224) exp(-373 K/T) cm(3) molecule(-1) s(-1). An ab initio potential energy surface was additionally used to derive a theoretical expression for this reaction.