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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 $Δλ\geλ/11600$, 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 $σ=0.03$ and 0.02~dex, respectively. The S/O, Ne/O, Ar/O, and Cl/O abundance ratios are very similar in both clouds, with $σ=0.02$-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, $σ=0.05$~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.