  This is a continuous work of our previous paper. In the previous work we
showed a triviality of the torsors in the case where period domains are
Hermitian symmetric and a non-triviality for one-example. In this paper we
determine whether the torsors are trivial or not for any period domains for
pure Hodge structures. We also show a generalization of a previous result which
gives a non-triviality on some open sets connecting to cycle spaces.
