  We study the isotropy representation of real flag manifolds associated to
simple Lie algebras that are split real forms of complex simple Lie algebras.
For each Dynkin diagram the invariant irreducible subspaces for the compact
part of the isotropy subgroup are described. Contrary to the complex flag
manifolds the decomposition into irreducible components is not in general
unique, since there are cases with infinitely many invariant subspaces.
