  A 1-parameter variation of Hodge structures corresponds to a holomorphic,
horizontal, locally liftable map into a classifying space of Hodge structures.
In this paper it is shown that such a map has a limit in the reductive
Borel-Serre compactification of the classifying space. The boundary component
in which the limit lies is a union over possible polarizations of classifying
spaces of Hodge structures on the primitive parts. It is discussed which
boundary components can contain such limit points.
