  We obtain strong information on the asymptotic behaviour of the counting
function for nilpotent Galois extensions with bounded discriminant of arbitrary
number fields. This extends previous investigations for the case of abelian
groups. In particular, the result confirms a conjecture by the second author on
this function for arbitrary groups in the nilpotent case. We further prove
compatibility of the conjecture with taking wreath products with the cyclic
group of order 2 and give examples in degree up to 8.
