O2(a 1Δg) production in a non-self-sustained discharge (ND) in pure oxygen and oxygen mixtures with inert gases (Ar and He) has been studied. A self-consistent model of ND in pure oxygen is developed, allowing us to simulate all the obtained experimental data. Agreement between the experimental and simulated results for pure oxygen over a wide range of reduced electric fields was reached only after taking into account the ion component of the discharge current. It is shown that the correct estimation of the energetic efficiency of O2(a 1Δg) excitation by discharge using the EEDF calculation is possible only with the correct description of the energy deposit into the plasma on the basis of an adequate discharge model. The testing of an O2(a 1Δg) excitation cross-section by direct electron impact, as well as a kinetic scheme of processes involving singlet oxygen, has been carried out by the comparison of experimental and simulated data. The tested model was then used for simulating O2(a 1Δg) production in ND in oxygen mixtures with inert gases. The study of O2(a 1Δg) production in Ar : O2 mixtures with small oxygen content has shown that the ND in these mixtures is spatially non-uniform, which essentially decreases the energetic efficiency of singlet oxygen generation. While simulating the singlet oxygen density dynamics, the process of three-body deactivation of O2(a 1Δg) by O(3P) atoms was for the first time taken into account. The maximal achievable concentration of singlet oxygen in ND can be limited by this quenching. On the basis of the results obtained and the model developed, the influence of hydrogen additives on singlet oxygen kinetics in argon–oxygen–hydrogen mixtures has been analysed. The simulation has shown that fast quenching of O2(a 1Δg) by atomic hydrogen is possible due to significant gas heating in the discharge that can significantly limit the yield of singlet oxygen in hydrogen-containing mixtures.