  We study the Oxygen and Nitrogen abundances in the interstellar medium of
high-redshift galaxies. We use high resolution and high signal-to-noise ratio
spectra of Damped Lyman-alpha (DLA) systems detected along the line-of-sight to
quasars to derive robust abundance measurements from unsaturated metal
absorption lines. We present results for a sample of 16 high-redshift DLAs and
strong sub-DLAs (log N(HI)>19.5, 2.4<zabs<3.6) including 13 new measurements.
We find that the Oxygen to Iron abundance ratio is pretty much constant with
[O/Fe]=+0.32+-0.10 for -2.5<[O/H]<-1.0 with a small scatter around this value.
The Oxygen abundance follows quite well the Silicon abundance within 0.2dex
although the Silicon abundance could be slightly smaller for [O/H]<-2. The
distribution of the [N/O] abundance ratio, measured from components that are
detected in both species, is somehow double peaked: five systems have [N/O]>-1
and nine systems have [N/O]<-1.15. In the diagram [N/O] versus [O/H], a loose
plateau is possibly present at [N/O]=-0.9 that is below the so-called primary
plateau as seen in local metal-poor dwarf galaxies ([N/O] in the range -0.57 to
-0.74). No system is seen above this primary plateau whereas the majority of
the systems lie well below with a large scatter. All this suggests a picture in
which DLAs undergo successive star-bursts. During such an episode, the [N/O]
ratio decreases sharply because of the rapid release of Oxygen by massive stars
whereas inbetween two bursts, Nitrogen is released by low and intermediate-mass
stars with a delay and the [N/O] ratio increases.
