  Oxygen abundances in a sample of ultra-metal-poor subdwarfs have been derived
from measurements of the oxygen triplet at 7771--5 A and OH lines in the near
UV performed in high-resolution and high signal-to-noise spectra obtained with
WHT/UES, KeckI/HIRES, and VLT/UVES. Our Fe abundances were derived in LTE and
then corrected for NLTE effects following Thevenin and Idiart (1999). The new
oxygen abundances confirm previous findings for a progressive linear rise in
the oxygen-to-iron ratio with a slope -0.33+-0.02 from solar metallicity to
[Fe/H] -3. A slightly higher slope would be obtained if the Fe NLTE corrections
were not considered. Below [Fe/H]= -2.5 our stars show [O/Fe] ratios as high as
~ 1.17 (G64-12), which can be interpreted as evidence for oxygen overproduction
in the very early epoch of the formation of the halo, possibly associated with
supernova events with very massive progenitor stars. We show that the arguments
against this linear trend given by Fulbright and Kraft (1999), based on the LTE
Fe analysis of two metal-poor stars cannot be sustained when an NLTE analysis
is performed. Using 1-D models our analysis of three oxygen indicators
available for BD +23 3130 gives consistent abundances within 0.16 dex and
average [O/Fe] ratio of 0.91.
