  We apply the recent derivations of dual charges in asymptotically flat
spacetimes to asymptotically locally AdS spacetimes. In contrast to the results
in the flat case, in the AdS case with a Dirichlet boundary the dual charge
contribution vanishes at the leading order. However, by focusing on the
Taub-NUT-AdS solution, we show that nevertheless, more generally, the dual
charge is non-vanishing and corresponds to the NUT parameter. We propose a
complex first law of black mechanics in the presence of NUT charges that is
inspired by the naturally complex nature of the charges derived using
Hamiltonian methods.
