Context :

Aims : We study the Oxygen and Nitrogen abundances in the interstellar medium of high-redshift galaxies .

Methods : 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 .

Results : We present results for a sample of 16 high-redshift DLAs and strong sub-DLAs ( log N ( H i ) > 19.5 , 2.4 < z _ { abs } < 3.6 ) including 13 new measurements .
We find that the Oxygen to Iron abundance ratio is pretty much constant with [ O/Fe ] \sim +0.32 \pm 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 \sim 0.2 dex 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 ] \sim - 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 .

Conclusions :