Spectroscopic observations obtained with the VLT of one planetary nebula ( PN ) in Sextans A and of five PNe in Sextans B and of several H ii regions in these two dwarf irregular galaxies are presented . The extended spectral coverage , from 320.0 to 1000.0 nm , and the large telescope aperture allowed us to detect a number of emission lines , covering more than one ionization stage for several elements ( He , O , S , Ar ) . The electron temperature diagnostic [ O iii ] line at 436.3 nm was measured in all six PNe and in several H ii regions allowing for an accurate determination of the ionic and total chemical abundances by means of the Ionization Correction Factors method . For the time being , these PNe are the farthest ones where such a direct measurement of the electron temperature is obtained . In addition , all PNe and H ii regions were also modelled using the photoionization code CLOUDY ( Ferland et al . [ 1998 ] ) . The physico-chemical properties of PNe and H ii regions are presented and discussed . A small dispersion in the oxygen abundance of H ii regions was found in both galaxies : 12 + \log ( O/H ) =7.6 \pm 0.2 in Sextans A , and 7.8 \pm 0.2 in Sextans B . For the five PNe of Sextans B , we find that 12 + \log ( O/H ) =8.0 \pm 0.3 , with a mean abundance consistent with that of H ii regions . The only PN known in Sextans A appears to have been produced by a quite massive progenitor , and has a significant nitrogen overabundance . In addition , its oxygen abundance is 0.4 dex larger than the mean abundance of H ii regions , possibly indicating an efficient third dredge-up for massive , low-metallicity PN progenitors . The metal enrichment of both galaxies is analyzed using these new data .