  We consider vortices in the nonlocal two-dimensional Gross-Pitaevskii
equation with the interaction potential having the Lorentz-shaped dependence on
the relative momentum. It is shown that in the Fourier series expansion with
respect to the polar angle the unstable modes of the axial $n$-fold vortex have
orbital numbers $l$ satisfying $0<|l|<2|n|$, similar as in the local model.
Numerical simulations show that nonlocality slightly decreases the threshold
rotation frequency above which the nonvortex state ceases to be the global
energy minimum and decreases the frequency of the anomalous mode of the
1-vortex. In the case of higher axial vortices, nonlocality leads to the
instability against splitting with creation of antivortices and gives rise to
additional anomalous modes with higher orbital numbers. Despite new instability
channels with creation of antivortices, for a stationary solution comprised of
vortices and antivortices there always exist another vortex solution, comprised
solely of vortices, with the same total vorticity but with a lower energy.
