  We study the dynamics of two types of pairs of excitations which are bound
despite their strong repulsive interaction. One corresponds to doubly occupied
sites in one-dimensional Bose-Hubbard systems, the so-called doublons. The
other is pairs of neighboring excited spins in anisotropic Heisenberg spin-1/2
chains. We investigate the possibility of decay of the bound pairs due to
resonant scattering by a defect or due to collisions of the pairs. We find that
the amplitudes of the corresponding transitions are very small. This is a
result of destructive quantum interference and explains the stability of the
bound pairs.
