Aims. We investigate two successive trains of large amplitude transverse oscillations in an arched EUV prominence, observed with SoHO/EIT on the north-east solar limb on 30 July 2005. The oscillatory trains are triggered by two large scale coronal waves, associated with an X-class and a C-class flare occurring in the same remote active region. Methods. The oscillations are tracked within rectangular slits parallel to the solar limb at different heights, which are taken to move with the apparent height profile of the prominence to account for solar rotation. Time series for the two prominence arch legs are extracted using Gaussian fitting on the 195 Å absorption features, and fitted to a damped cosine curve to determine the oscillatory parameters.Results. Differing energies of the two triggering flares and associated waves are found to agree with the velocity amplitudes, of 50.6 ± 3.2 and 15.9 ± 8.0 km s −1 at the apex, for the first and second oscillatory trains respectively, as estimated in the transverse direction. The period of oscillation is similar for both trains, with an average of 99 ± 11 min, indicating a characteristic frequency as predicted by magnetohydrodynamics. Increasing velocity amplitude with height during the first oscillatory train, and in-phase starting motions of the two legs regardless of height, for each train, demonstrate that the prominence exhibits a global kink mode to a first approximation. However, discrepancies between the oscillatory characteristics of the two legs and an apparent dependence of period upon height, suggest that the prominence actually oscillates as a collection of separate but interacting threads. Damping times of around two to three cycles are observed. Combining our results with those of previously analysed loop oscillations, we find an approximately linear dependence of damping time upon period for kink oscillations, supporting resonant absorption as the damping mechanism despite limitations in testing this theory.