  In this paper we study the symmetries of the dual Taub-NUT metrics. Generic
and non-generic symmetries of dual Taub-NUT metrics are investigated.
  The existence of the Runge-Lenz type symmetry is analyzed for dual Taub-NUT
metrics.
  We find that in some cases the symmetries of the dual metrics are the same
with the symmetries of Taub-NUT metric.
