  A nilmanifold is a quotient N\G of a connected and simply connected nilpotent
Lie group G by a uniform lattice N. In this paper we determine the Reidemeister
and Nielsen number of affine n-valued maps on such a nilmanifold. These are
maps for which a given lifting to G splits into n affine maps of the Lie group
G. In order to obtain this result we also establish a way of computing the
number of generalized twisted conjugacy classes on finitely generated torsion
free nilpotent groups.
