  We present deep echelle spectrophotometry of the Galactic HII region NGC
2579. The data have been taken with the Very Large Telescope Ultraviolet-Visual
Echelle Spectrograph in the 3550--10400 \AA\ range. This object, which has been
largely neglected, shows however a rather high surface brightness, a high
ionization degree and is located at a galactocentric distance of 12.4 $\pm$ 0.7
kpc. Therefore, NGC 2579 is an excellent probe for studying the behaviour of
the gas phase radial abundance gradients in the outer disc of the Milky Way. We
derive the physical conditions of the nebula using several emission
line-intensity ratios as well as the abundances of several ionic species from
the intensity of collisionally excited lines. We also determine the ionic
abundances of C$^{2+}$, O$^+$ and O$^{2+}$ -- and therefore the total O
abundance -- from faint pure recombination lines. The results for NGC 2579
permit to extend our previous determinations of the C, O and C/O gas phase
radial gradients of the inner Galactic disc (Esteban etal. 2005) to larger
galactocentric distances. We find that the chemical composition of NGC 2579 is
consistent with flatten gradients at its galactocentric distance. In addition,
we have built a tailored chemical evolution model that reproduces the observed
radial abundance gradients of O, C and N and other observational constraints.
We find that a levelling out of the star formation efficiency about and beyond
the isophotal radius can explain the flattening of chemical gradients observed
in the outer Galactic disc.
