  Let ${\cal L}$ be a local system on the complement $X^{\star}$ of a normal
crossing divisor (NCD) $ Y$ in a smooth analytic variety $X$ and let $ j:
X^{\star} = X - Y \to X $ denotes the open embedding. The purpose of this paper
is to describe a weight filtration $W$ on the direct image ${\bf
j}_{\star}{\cal L} $ and in case a morphism $f: X \to D$ to a complex disc is
given with $Y = f^{-1}(0)$, the weight filtration on the complex of nearby
cocycles $\Psi_f ({\cal L})$ on $Y$. A comparison theorem shows that the
filtration coincides with the weight defined by the logarithm of the monodromy
and provides the link with various results on the subject.
