Oxygen molecules in the lowest metastable state, O-2(a(1)Delta(g)), play an important role in oxygen plasmas due to their high reactivity and significant concentrations. The accumulation of high densities of O-2(a(1)Delta(g)) occurs due to its low quenching rate. This paper demonstrates the existence, at high gas temperatures (700-1700 K), of fast quenching of O-2(a(1)Delta(g)) by O(P-3) atoms, a process that has not been considered in previous models. Experiments were carried out at oxygen pressures of 10-100 Torr in an 81 MHz CCP discharge in a quartz tube with external electrodes. This setup provides high absorbed power density, leading to both high gas temperatures and significant O(P-3) densities. We observe that the O-2(a(1)Delta(g)) density is significantly limited at high gas temperatures by rapid quenching by atomic oxygen. The results were interpreted using a self-consistent 1D discharge model. The observations can only be explained by the inclusion of a rapid quenching reaction: O-2(a(1)Delta(g)) + O(P-3) -> O-2(X-3 sigma(-)(g)) + O(P-3), with an activation energy in the range of 0.54-0.69 eV. The rate constant was determined over a wide range of discharge conditions (P = 20-100 Torr and T-g = 800-1700 K), giving values between 3 x 10(-11) exp(-8000/T) cm(3) s(-1) to 1.5 x 10(-11) exp(-6300/T) cm(3) s(-1). A possible mechanism for this process is discussed. Measurements of the density of metastable O-2(b(1)sigma(+)(g)) molecules also indicated the existence of quenching by atomic oxygen, with a somewhat lower activation energy of similar to 0.32 eV. The variations of the measured [O-2(b(1)sigma(+)(g))]/N mole-fraction could be fitted by the model using a rate constant 2 x 10(-11) x exp(-3700/T) cm(3) s(-1) for this process. These quenching processes of metastable O-2(a(1)Delta(g)) and O-2(b(1)sigma(+)(g)) molecules by oxygen atoms are important for oxygen plasmas and could have a significant impact on the kinetics of oxygen-containing mixtures at higher gas temperatures, for example in plasma-assisted combustion or in high-pressure plasma processing reactors.