  Using high resolution cosmological N-body simulations, we investigate the
survival of dark matter satellites falling into larger haloes. Satellites
preserve their identity for some time after merging. We compute their loss of
mass, energy and angular momentum as dynamical friction, tidal forces and
collisions with other satellites dissolve them. We also analyse the evolution
of their internal structure. Satellites with less than a few per cent the mass
of the main halo may survive for several billion years, whereas larger
satellites rapidly sink into the center of the main halo potential well and
lose their identity. Penetrating encounters between satellites are frequent and
may lead to significant mass loss and disruption. Only a minor fraction of
cluster mass (10 per cent on average) is bound to substructure at most
redshifts of interest. We discuss the application of these results to the
survival and extent of dark matter haloes associated with cluster galaxies, and
to interactions between galaxies in clusters. We find that 35-40 per cent of
galaxy dark matter haloes are disrupted by the present time. The fraction of
satellites undergoing close encounters is similar to the fraction of
interacting or merging galaxies in clusters at moderate redshift.
