ZZ Ceti stars form the most numerous group of degenerate variable stars. They are otherwise normal DA (H-rich atmospheres) white dwarfs that exhibit pulsations. Here, we present an asteroseismological analysis for 44 bright ZZ Ceti stars based on a new set of fully evolutionary DA white dwarf models characterized by detailed chemical profiles from the centre to the surface. One of our targets is the archetypal ZZ Ceti star G117−B15A, for which we obtain an asteroseismological model with an effective temperature and a surface gravity in excellent agreement with the spectroscopy. The asteroseismological analysis of a set of 44 ZZ Ceti stars has the potential to characterize the global properties of the class, in particular the thicknesses of the hydrogen envelope and the stellar masses. Our results support the belief that white dwarfs in the solar neighbourhood harbour a broad range of hydrogen-layer thickness.