  We consider universal methods for obtaining (uniform) continuity bounds for
characteristics of multipartite quantum systems. We pay a special attention to
infinite-dimensional multipartite quantum systems under the energy constraints.
  By these methods we obtain continuity bounds for several important
characteristics of a multipartite quantum state: the quantum (conditional)
mutual information, the squashed entanglement, the c-squashed entanglement and
the conditional entanglement of mutual information. The continuity bounds for
the multipartite quantum mutual information are asymptotically tight for large
dimension/energy.
  The obtained results are used to prove the asymptotic continuity of the
$n$-partite squashed entanglement, c-squashed entanglement and the conditional
entanglement of mutual information under the energy constraints.
