The production and transport dynamics of O-2(a(1)Delta(g)) and O-2(b(1)Sigma(g)(+)) molecules as well as O(P-3) atoms has been studied in an O-2 flow excited by a 13.56 MHz RF discharge in a quartz tube at pressures of 1-20 Torr. It has been shown that the densities of O-2(a(1)Delta(g)) and O(P-3) are saturated with increasing energy input into the discharge. The maximum yield of singlet oxygen (SO) and the O-2 dissociation degree drops with pressure. It is demonstrated that depending on the energy input the RF discharge can exist in three modes: I-in the spatially homogeneous mode or alpha-mode; III-in the substantially inhomogeneous mode, when plasma jets are present outside the discharge; and II-in the transient mode between modes I and III. In this paper only the homogeneous mode of RF discharge in the O-2 flow is considered in detail. A self-consistent model of the a-mode is developed, that allows us to analyse elementary processes responsible for the production and loss of O-2(a(1)A(g)) and O-2(b(1)Sigma(g)(+)) molecules as well as O(P-3) atoms in detail. To verify both the kinetic scheme of the model and the conclusions, some experiments have been carried out at lower flow velocities and higher pressures (>= 10 Torr), when the stationary densities of O-2(a(1)Delta(g)), O-2(b(1)Sigma(g)(+)) and O(P-3) in the discharge area were established not by the escape of particles but by the losses due to the volumetric and surface reactions. The O-2(b(1)Sigma(g)(+)) density under these conditions is determined by the balance of O-2(b(1)Sigma(g)(+)) production by both direct electron impact and electronic excitation transfer from metastable O(D-1) atoms and deactivation by oxygen atoms and tube walls, including quenching by ozone in the afterglow. The O(P-3) density is determined by the balance between the production through O-2 dissociation by electron impact and heterogeneous loss at the wall recombination. The stationary density of O-2(a(1)Delta(g)) is provided by the processes of O-2(a(1)Delta(g)) production by direct electron impact and loss owing to quenching by the tube walls at a low pressure below 4 Torr, as well as by three-body recombination with oxygen atoms with increasing pressure above 7 Torr. The analysis of with increasing pressure above 7 Torr. The analysis of O-2(a(1)Delta(g)) three-body quenching by oxygen atoms showed that this process could actually have a high rate constant and be able to provide a fast SO deactivation at high pressures. The approximate value of the rate constant-(1-3) x 10(-32) cm(3) s(-1) has been obtained from the best agreement between the simulated and experimental data on transport dynamics of O-2(a(1)Delta(g)) molecules and O(P-3) atoms. It is shown that the RF discharge a-mode corresponds to a discharge with an effective reduced electrical field in a quasi-neutral plasma of about similar to 30 Td, which makes possible a rather high efficiency of SO production of similar to 3-5%.