The pulsating DA white dwarfs (ZZ Ceti stars) are $g$-mode non-radial pulsators. Asteroseismology provides strong constraints on their global parameters and internal structure. Since all the DA white dwarfs falling in the ZZ Ceti instability strip do
pulsate, the internal structure derived from asteroseismology brings knowledge for the DA white dwarfs as a whole group. HS 0507+0434B is one of the ZZ Ceti stars which lies approximately in the middle of the instability strip for which we have undertaken a detailed asteroseismological study. We carried out multisite observation campaigns in 2007 and from December 2009 to January 2010. In total, 206 hours of photometric time-series have been collected. They have been analysed by means of Fourier analysis and simultaneous multi-frequency sine-wave fitting. In total, 39 frequency values are resolved including 6 triplets and a number of linear combinations. We identify the triplets as $ell$=1 $g$-modes split by rotation. We derived the period spacing, the rotational splitting and the rotation rate. From the comparison of the observed periods with the theoretical periods of a series of models we estimate the fundamental parameters of the star: its total mass M$_{*}$/M$_{odot}$ = 0.675, its luminosity L/L$_{odot}$=3.5$times 10^{-3}$, and its hydrogen mass fraction M$_{H}$/M$_{*}$= 10$^{-8.5}$.
We present an analysis of the observations of HD 51106 and HD 50747 by the satellite CoRoT, obtained during its initial run, and of the spectroscopic preparatory observations. AIMS: We complete an analysis of the light curve, extract the main frequ
encies observed, and discuss some preliminary interpretations about the stars. Methods: We used standard Fourier transform and pre-whitening methods to extract information about the periodicities of the stars. Results: HD 51106 is an ellipsoidal binary, the light curve of which can be completely explained by the tidal deformation of the star and smaller secondary effects. HD 50747 is a triple system containing a variable star, which exhibits many modes of oscillation with periods in the range of a few hours. On the basis of this period range and the analysis of the physical parameters of the star, we conclude that HD 50747 is a Gamma-Doradus star.
