  The aim of this article is to study degeneration of the variations of Hodge
structure associated to a proper K\"ahler semistable morphism. We prove that
the weight filtrations constructed in the author's previous paper coincide with
the monodromy weight filtrations on the relative log de Rham cohomology groups
of a proper K\"ahler semistable morphism. Moreover, we show that the limiting
mixed Hodge structures form admissible variations of mixed Hodge structure.
