  We present the results of Monte Carlo simulations for the antiferromagnetic
classical XXZ model with easy-plane exchange anisotropy on the triangular
lattice, which causes frustration of the spin alignment. The behaviour of this
system is similar to that of the antiferromagnetic XY model on the same
lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition,
associated to vortex-antivortex unbinding, and of an Ising-like one due to the
chirality, the latter occurring at a slightly higher temperature. Data for
internal energy, specific heat, magnetic susceptibility, correlation length,
and some properties associated with the chirality are reported in a broad
temperature range, for lattice sizes ranging from 24x24 to 120x120; four values
of the easy-plane anisotropy are considered. Moving from the strongest towards
the weakest anisotropy (1%) the thermodynamic quantities tend to the isotropic
model behaviour, and the two transition temperatures decrease by about 25% and
22%, respectively.
