  In this paper I continue the study of the new framework of modular
localization and its constructive use in the nonperturbative d=1+1
Karowski-Weisz-Smirnov formfactor program. Particular attention is focussed on
the existence of semilocal generators of the wedge-localized algebra without
vauum polarization (FWG-operators) which are closely related to objects
fulfilling the Zamolodchikov-Faddeev algebraic structure. They generate a
``thermal Hilbert space'' and allow to understand the equivalence of the KMS
conditions with the so-called cyclicity equation for formfactors which was
known to be closely related to crossing symmetry properties. The modular
setting gives rise to interesting new ideas on ``free'' d=2+1 anyons and
plektons.
