  With the aim of setting constraints for the modeling of the QCD phase
diagram, the phase structure of the two-flavor Polyakov-loop extended Nambu and
Jona-Lasinio (PNJL) model is investigated in the range of imaginary chemical
potentials ($\mu_\mathrm{I}$) and compared with available $N_f=2$ lattice QCD
results. The calculations are performed using the advanced nonlocal version of
the PNJL model with the inclusion of vector-type quasiparticle interactions
between quarks, and with wave-function-renormalization corrections. It is
demonstrated that the nonlocal PNJL model reproduces important features of QCD
at finite $\mu_\mathrm{I}$, such as the Roberge-Weiss (RW) periodicity and the
RW transition. Chiral and deconfinement transition temperatures for $N_f=2$
turn out to coincide both at zero chemical potential and at finite
$\mu_\mathrm{I}$. Detailed studies are performed concerning the RW endpoint and
its neighborhood where a first-order transition occurs.
