The kinetics of reactions of the OH radical with ethene, ethyne (acetylene), propyne (methyl acetylene) and t-butyl-hydroperoxide were studied at temperatures of 69 and 86 K using laser flash-photolysis combined with laser-induced fluorescence spectroscopy. A new pulsed Laval nozzle apparatus is used to provide the low-temperature thermalised environment at a single density of 4 × 1016 molecule cm-3 in N2. The density and temperature within the flow are determined using measurements of impact pressure and rotational populations from laser-induced fluorescence spectroscopy of NO and OH. For ethene, rate coefficients were determined to be k2 = (3.22 ± 0.46) × 10-11 and (2.12 ± 0.12) × 10-11 cm3 molecule-1 s-1 at T = 69 and 86 K, respectively, in good agreement with a master-equation calculation utilising an ab initio surface recently calculated for this reaction by Cleary et al. (P. A. Cleary, M. T. Baeza Romero, M. A. Blitz, D. E. Heard, M. J. Pilling, P. W. Seakins and L. Wang, Phys. Chem. Chem. Phys., 2006, 8, 5633-5642) For ethyne, no previous data exist below 210 K and a single measurement at 69 K was only able to provide an approximate upper limit for the rate coefficient of k3 < 1 × 10-12 cm3 molecule-1 s-1, consistent with the presence of a small activation barrier of 5 kJ mol-1 between the reagents and the OH-C2H2 adduct. For propyne, there are no previous measurements below 253 K, and rate coefficients of k4 = (5.08 ± 0.65), (5.02 ± 1.11) and (3.11 ± 0.09) × 10-12 cm3 molecule-1 s-1 were obtained at T = 69, 86 and 299 K, indicating a much weaker temperature dependence than for ethene. The rate coefficient k1 = (7.8 ± 2.5) × 10-11 cm3 molecule-1 s-1 was obtained for the reaction of OH with t-butyl-hydroperoxide at T = 86 K. Studies of the reaction of OH with benzene and toluene yielded complex kinetic profiles of OH which did not allow the extraction of rate coefficients. Uncertainties are quoted at the 95% confidence limit and include systematic errors.