It is known that self-shielding of UV radiation by 16O2 produces selective isotopic effects upon photodissociation. An analysis of this process and the chemical kinetics of isotopic exchange and trapping of O has been carried out for different gas compositions and temperatures. Calculations of the shift in 16O, 17O, 18O abundances due to self-shielding were carried out, and it is shown that the specific rates of photodissociation Ji give J17 J18 ∼ 1 for column densities of O2 between ∼ 1019 and 1022 molecules/cm2 with a maximum value of J17 J16 = 11 at a column density of ∼ 1021 molecules/cm2. The O produced in this manner would have 17O 18O close to the starting material but be depleted in 16O. These large shifts are quenched at temperatures higher than 500 K, or if water is present in higher concentration than O2. Following dissociation, fast isotopic exchange reactions (e.g. 17O + 16O2 → 16O + 17O16O) may destroy the effect unless the atomic oxygen is efficiently trapped. Competition between trapping and exchange is shown to be of a simple mathematical form which depends on the ratio of the rate of trapping of O to the rate of exchange. Using known rate constants it is shown that trapping of anomalous O by metal atoms, hydrogen, or the O2 itself is inefficient at pressures lower than 10-3 atm and normal solar abundances. Trapping on dust grains may be efficient if all oxides are present as sub-micron particles. However, the extinction of radiation by the dust is likely to quench the self-shielding effect itself. Self-shielding of radiation by O2, may, under special conditions, lead to the production of isotopically anomalous products. However, in the light of the difficulties throughout many stages of the process, it appears to be an unsatisfactory explanation for the oxygen anomalies observed in meteorites. The above considerations are also applied to two experiments where O is trapped by O2 to form ozone. The isotopic shifts found in experiments by Sander et al.  in O3 are compatible with the criteria developed here. The shifts found by Thiemens and Heidenreich [11,12] using a discharge cannot be explained by self-shielding of UV radiation as the pressure is below the minimum needed for self-shielding to occur. The general nature of the pressure dependence of recent discharge experiments by Thiemens and others is in agreement with the prediction of a simple kinetic model based on the production of isotopically anomalous O during dissociation of O2, isotopic exchange of O and O2, and ozone formation. The observed isotopic effects in O3 produced and trapped during discharge in O2 thus appear to be understood phenomenologically but the mechanism for selective isotopic dissociation of O2 is still obscure and remains a fundamental problem. Our analysis is directed toward O2-rich environments and may only have limited applicability in the environment of the solar nebula. However, the general approach presented here is useful and may be applied to CO. It appears that selective isotopic shielding, or the mechanism which operates in the discharge experiments may still provide an explanation for some isotopic effects observed in meteorites but only if rapid trapping and isolation mechanisms (relative to exchange) can be found which apply in a low-pressure regime.