  We present high signal-to-noise spectrophotometric observations of seven
luminous HII galaxies. The observations have been made with the use of a
double-arm spectrograph which provides spectra with a wide wavelength coverage,
from 3400 to 10400\AA free of second order effects, of exactly the same region
of a given galaxy. These observations are analysed applying a methodology
designed to obtain accurate elemental abundances of oxygen, sulphur, nitrogen,
neon, argon and iron in the ionized gas. Four electron temperatures and one
electron density are derived from the observed forbidden line ratios using the
five-level atom approximation. For our best objects errors of 1% in
t_e([OIII]), 3% in t_e([OII]) and 5% in t_e([SIII]) are achieved with a
resulting accuracy of 7% in total oxygen abundances, O/H.
  The ionisation structure of the nebulae can be mapped by the theoretical
oxygen and sulphur ionic ratios, on the one side, and the corresponding
observed emission line ratios, on the other -- the \eta and \eta' plots --. The
combination of both is shown to provide a means to test photo-ionisation model
sequences currently applied to derive elemental abundances in HII galaxies.
