  In this paper, we prove a generalization of Reznikov's theorem which says
that the Chern-Simons classes and in particular the Deligne Chern classes (in
degrees $>1$) are torsion, of a flat bundle on a smooth complex projective
variety. We consider the case of a smooth quasi--projective variety with an
irreducible smooth divisor at infinity. We define the Chern-Simons classes of
Deligne's canonical extension of a flat vector bundle with unipotent monodromy
at infinity, which lift the Deligne Chern classes and prove that these classes
are torsion.
