  In [arXiv:0803.3259] the equations describing the parallel transport of
orthonormal frames along timelike (spacelike) geodesics in a spacetime
admitting a non-degenerate principal conformal Killing-Yano 2-form h were
solved. The construction employed is based on studying the Darboux subspaces of
the 2-form F obtained as a projection of h along the geodesic trajectory. In
this paper we demonstrate that, although slightly modified, a similar
construction is possible also in the case of null geodesics. In particular, we
explicitly construct the parallel-transported frames along null geodesics in
D=4,5,6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport
along principal null directions in these spacetimes. Such directions coincide
with the eigenvectors of the principal conformal Killing-Yano tensor. Finally,
we show how to obtain a parallel-transported frame along null geodesics in the
background of the 4D Plebanski-Demianski metric which admits only a conformal
generalization of the Killing-Yano tensor.
