  Like its precursor this paper is concerned with the Hopf algebra of
noncommutative symmetric functions and its graded dual, the Hopf algebra of
quasisymmetric functions. It complements and extends the previous paper but is
also selfcontained. Here we concentrate on explicit descriptions
(constructions) of a basis of the Lie algebra of primitives of NSymm and an
explicit free polynomial basis of QSymm. As before everything is done over the
integers. As applications the matter of the existence of suitable analogues of
Frobenius and Verschiebung morphisms is discussed.
