  In [8,9], the authors developed a nice formula to compute the Nielsen number
of a self-map on an infra-nilmanifold. For the case of nilmanifolds this
formula was extended to $n$-valued maps in [4]. In this paper, we extend these
results further and establish the averaging formula to compute the Nielsen
number of any $n$-valued affine map on an infra-nilmanifold.
