  We use very deep spectra obtained with the Ultraviolet-Visual Echelle
Spectrograph at the Very Large Telescope to derive physical conditions and
chemical abundances of four H II regions of the Large Magellanic Cloud (LMC)
and four H II regions of the Small Magellanic Cloud (SMC). The observations
cover the spectral range 3100-10400 \A with a spectral resolution of
$\Delta\lambda\ge\lambda/11600$, and we measure 95-225 emission lines in each
object. We derive ionic and total abundances of O, N, S, Ne, Ar, Cl, and Fe
using collisionally excited lines. We find average values of
$12+\log(\mbox{O/H})=8.37$ in the LMC and $8.01$ in the SMC, with standard
deviations of $\sigma=0.03$ and 0.02~dex, respectively. The S/O, Ne/O, Ar/O,
and Cl/O abundance ratios are very similar in both clouds, with
$\sigma=0.02$-0.03~dex, which indicates that the chemical elements are well
mixed in the interstellar medium of each galaxy. The LMC is enhanced in N/O by
$\sim0.20$~dex with respect to the SMC, and the dispersions in N/O,
$\sigma=0.05$~dex in each cloud, are larger than those found for the other
elements. The derived standard deviations would be much larger for all the
abundance ratios, up to 0.20~dex for N/O, if previous spectra of these objects
were used to perform the analysis. Finally, we find a wide range of iron
depletions in both clouds, with more than 90 per cent of the iron atoms
deposited onto dust grains in most objects.
