On the Accuracy in the Derivation of Elemental Abundances in HII Galaxies

We propose a methodology to perform a self-consistent analysis of the physical properties of the nebular material of HII galaxies adequate to the data that can be obtained with the XXI century technology. This methodology requires the production and calibration of empirical relations between the different line temperatures that should superseed the currently used ones based on very simple, and poorly tested, photo-ionization model sequences. The analysis of spectroscopic data covering from 3200 to 10500 angstroms , allows a careful and realistic treatment of the observational errors and combined with state of the art models yields total oxygen abundances with accuracies between 5 and 9 %. These accuracies are expected to improve as better calibrations based on more precise measurements, both on electron temperatures and densities, are produced.