In this work, we investigated the self-reaction of allyl radicals and its cross-reaction with hydroxyl radical by employing shock tube and laser absorption techniques. We carried out the experiments behind reflected shock waves over the temperature range of 800-1200 K and pressures of 1.1-2.5 bar. We generated allyl (CH) and OH radicals by fast thermal decomposition of allyl iodide (CHI) and tert-butyl hydroperoxide (TBHP), respectively, and monitored reaction progress by detecting OH near 306.69 nm and CH near 220 nm using UV laser absorption. At the detection wavelength, we measured the temperature dependence of the absorption cross-sections of CH and CHI. Rate coefficient for the self-recombination reaction of allyl radicals showed a small negative temperature dependence and no noticeable fall-off behavior over 1.15-1.96 bar giving a mean value of kC3H5+C3H5=(1.0±0.2)×10-11cm3molecule-1s-1. Likewise, the cross-reaction of allyl and OH radicals did not exhibit discernible pressure and temperature dependence under our experimental conditions indicating a barrierless reaction, and an average value of kC3H5+OH=(9.3±0.7)×10-11cm3molecule-1s-1 best illustrates our measured rate coefficients. These measurements represent the first direct experimental determinations of the rate coefficients for these important radical-radical reactions at high temperatures and pressures.