  We consider the moduli space MN of flat unitary connections on an open
Kaehler manifold U (complement of a divisor with normal crossings) with
restrictions on their monodromy transformations. Using intersection and L2
cohomologies with degenerating coefficients we construct a natural symplectic
form F on MN. When U is quasi-projective we prove that F is actually a Kaehler
form.
