  Let $f\colon X\to Y$ be a semistable fibration between smooth complex
varieties of dimension $n$ and $m$. This paper contains an analysis of the
local systems of de Rham closed relative one forms and top forms on the fibers.
In particular the latter recovers the local system of the second Fujita
decomposition of $f_*\omega_{X/Y}$ over higher dimensional base. The so called
theory of Massey products allows, under natural Castelnuovo-type hypothesis, to
study the finiteness of the associated monodromy representations. Motivated by
this result, we also make precise the close relation between Massey products
and Castelnuovo-de Franchis type theorems.
