  Here we extend the approach developed in \cite{adel_2} to study the
thermodynamics of Taub-NUT-AdS and dyonic Taub-NUT-AdS solutions. Furthermore,
we investigate in details the possible phase structures of the dyonic
Taub-NUT-AdS solution. We show that the first law, Gibbs-Duhem and Smarr's
relations are all satisfied for both solutions. Our study of phase structures
shows some intriguing features, which were not reported before, among which the
existence of two distinguished critical points with a region of continuous
phase transitions in between, and the possibility of merging them into one
point. To analyze these phases we consider both canonical and mixed ensembles.
The two distinguished critical points occur for the canonical case as well as
the mixed cases with $1/2 \le \phi_e < 1$. Another interesting case is the
mixed ensemble with $\phi_e \ge 1$, where we have one critical point but the
continuous phase transition region in the $P-T$ diagram is close to the origin,
in contrast with what happens in Reissner-Nordstrom-AdS solutions and Van der
Waals fluids, i.e., the continuous phase transition happens only for low enough
pressures and temperatures!
