Context. During complex and long duration solar flares, several filament destabilizations or eruptions can occur that are often related to coronal mass ejections (CMEs). Aims. We describe the study of an X3.8 long duration event (LDE) that occurred in NOAA 10720 on 17 January 2005 and was characterized by three filament destabilizations and two CMEs. Methods. Using multi-wavelength data provided by both ground-based instruments and satellites, in addition to MDI magnetograms, we investigated the morphological and magnetic evolution of the active region before and during the LDE. Results. Our analysis of H α and 1600 Å images showed that initially a two-ribbon structure developed in the central part of the active region, where a filament was previously observed. At a later time, two bright ribbons (in the most eastern side) and a strong brightness increase (at the western outskirt of the active region) were simultaneously observed. In a subsequent time interval, a new pair of ribbons was observed in the western side of the active region. Moreover, a linear force-free field extrapolation helped identify a null point in the central part of the active region. Conclusions. The initial filament destabilization that occurred in the central part of NOAA 10720 was probably due to magnetic flux emergence and photospheric shearing motions, which caused a slow tether-cutting process beneath the filament. The rearrangement of the magnetic field configuration, occurring in the same area as the location of the null point, changed the magnetic field connectivity in the active region, triggering two filament eruptions in the eastern and western part of the active region and two halo CMEs, in a kind of domino effect.