  We prove that iterated Whitehead products of length (n+1) vanish in any value
of an n-excisive functor in the sense of Goodwillie. We compare then different
notions of homotopy nilpotency, from the Berstein-Ganea definition to the
Biedermann-Dwyer one. The latter is strongly related to Goodwillie calculus and
we analyze the vanishing of iterated Whitehead products in such objects.
