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We report the results of a non-LTE Fe, O and Mg abundance analysis of thecarbon-nitrogen-rich ultra-metal-poor giants CS29498--043 and CS22949--037. Theabundance of oxygen has been derived from measurements of the oxygen triplet at7771-5 A in high resolution spectra obtained with KeckI/HIRES and the forbiddenline [OI] 6300 A detected in the TNG/SARG spectra of CS29498-043. Detailednon-LTE analysis of Fe lines has provided reliable stellar parameters which,however, do not resolve the oxygen abundance conflict as derived from the OI7771-5 A triplet and the [OI] 6300 A forbidden lines. We obtained the followingoxygen abundance: for CS22949-037 [O/Fe] =3.13, 1.95; and for CS29498-043;[O/Fe]=3.02, 2.49, based on the OI 7771-5 A triplet and the [OI] 6300 Aforbidden line, respectively. A similar conflict appears to exist between theforbidden resonance line MgI 4571 A and several subordinate lines, such as MgI5172 and 5183 A. Our analysis demonstrates the failure of standardplane--parallel atmosphere models to describe the physical conditions in theline-forming regions of these ultra-metal-poor giants.Comment: 16 pages, 15 figures, accepted by Astronomy and Astrophysic

Oxygen and magnesium abundance in the ultra-metal-poor giants CS 22949-037 and CS 29498-043: Challenges in models of atmospheres