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Let $\mathbb{F}_{\Theta }=G/P_{\Theta }$ be a flag manifold associated to anon-compact real simple Lie group $G$ and the parabolic subgroup $% P_{\Theta}$. This is a closed subgroup of $G$ determined by a subset $% \Theta $ ofsimple restricted roots of $\mathfrak{g}=Lie(G)$. This paper computes thesecond de Rham cohomology group of $\mathbb{F}_\Theta$. We prove that it zeroin 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 closed2-forms as characteristic classes of principal fiber bundles. The startingpoint is the computation of the second homology group of $\mathbb{F}_{\Theta }$with coefficients in a ring $R$.

De Rham $2$-cohomology of real flag manifolds