In this paper we study the oxygen chemistry in the C-rich circumstellar shells of IRC+10216. The recent discoveries of oxygen bearing species (water, hydroxyl radical and formaldehyde) toward this source challenge our current understanding of the chemistry in C-rich circumstellar envelopes. The presence of icy comets surrounding the star or catalysis on iron grain surfaces have been invoked to explain the presence of such unexpected species. This detailed study aims at evaluating the chances of producing O-bearing species in the C-rich circumstellar envelope only by gas phase chemical reactions. For the inner hot envelope, it is shown that although most of the oxygen is locked in CO near the photosphere (as expected for a C/O ratio greater than 1), some stellar radii far away species such as H2O and CO2 have large abundances under the assumption of thermochemical equilibrium. It is also shown how non-LTE chemistry makes very difficult the CO-->H2O,CO2 transformation predicted in LTE. Concerning the chemistry in the outer and colder envelope, we show that formaldehyde can be formed through gas phase reactions. However, in order to form water vapor it is necessary to include a radiative association between atomic oxygen and molecular hydrogen with a quite high rate constant. The chemical models explain the presence of HCO+ and predict the existence of SO and H2CS (which has been detected in a 3 mm line survey to be published). We have modeled the line profiles of H2CO, H2O, HCO+, SO and H2CS using a non-local radiative transfer model and the abundance profiles predicted by our chemical model. The results have been compared to the observations and discussed.Peer reviewed