Context. Titan’s stratosphere contains oxygen compounds (CO, CO2 , and H2 O), implying an external source of oxygen whose nature is still uncertain. Recent observations from the Herschel Space Observatory using the HIFI and PACS instruments and the Cassini /CIRS, as well as steady-state photochemical modeling indicate that the amounts of CO2 and H2 O in Titan’s stratosphere may imply inconsistent values of the OH/H2 O input flux, and that the oxygen source is time-variable.Aims. We attempt to reconcile the H2 O and CO2 observed profiles in Titan’s atmosphere by using an updated photochemical scheme and developing several time-dependent scenarios for the influx/evolution of oxygen species.Methods. We use a time-dependent photochemical model of Titan’s atmosphere to calculate effective lifetimes and the response of Titan’s oxygen compounds to changes in the oxygen input flux. Two variants for the C-H-O chemical network are considered. We investigate a time-variable Enceladus source and the evolution of material delivered by a cometary impact.Results. We find that the effective lifetime of H2 O in Titan’s atmosphere is only a factor of six shorter than that of CO2 and exceeds 10 yr below 200 km. A time-variable Enceladus source, involving a decrease by a factor of 5–20 in the OH/H2 O flux over the last few centuries, shows promise in explaining the relative CO2 /H2 O profiles. However, if the previous measurements from the Herschel Space Observatory are representative of Titan’s atmospheric water, an additional H2 O loss to the haze term is needed to bring the model in full agreement with the data. In an alternate situation, CO2 production following a cometary impact that occurred at least 220–300 yr ago can in principle explain the CO2 “excess” in Titan’s stratosphere, but this scenario is highly unlikely, given the estimates of the impact rate at Titan.