  This paper continues the same-named article, Part I (math.QA/9812083). We
give a global operator approach to the WZWN theory for compact Riemann surfaces
of an arbitrary genus g with marked points. Globality means here that we use
Krichever-Novikov algebras of gauge and conformal symmetries (i.e. algebras of
global symmetries) instead of loop and Virasoro algebras (which are local in
this context). The elements of this global approach are described in Part I. In
the present paper we give the construction of conformal blocks and the
projective flat connection on the bundle constituted by them.
