  Let $\mathbb{F}_{\Theta }=G/P_{\Theta }$ be a flag manifold associated to a
non-compact real simple Lie group $G$ and the parabolic subgroup $% P_{\Theta
}$. This is a closed subgroup of $G$ determined by a subset $% \Theta $ of
simple restricted roots of $\mathfrak{g}=Lie(G)$. This paper computes the
second de Rham cohomology group of $\mathbb{F}_\Theta$. We prove that it zero
in general, with some rare exceptions. When it is non-zero, we give a basis of
$H^2(\mathbb{F}_\Theta,\mathbb{R})$ through the Weil construction of closed
2-forms as characteristic classes of principal fiber bundles. The starting
point is the computation of the second homology group of $\mathbb{F}_{\Theta }$
with coefficients in a ring $R$.
