  Necessary and sufficient conditions for reducidibility of a self-adjoint
linear relation in a Krein space are given. Then a generalized Nevanlinna
function $Q$, represented by a self-adjoint linear relation $A$, is decomposed
by means of the reducing subspaces of $A$. The sum of two functions $Q_{i}{\in
N}_{\kappa_{i}}\left( \mathcal{H} \right),\thinspace i=1,\thinspace 2$,
minimally represented by the triplets $\left( \mathcal{K}_{i},A_{i},\Gamma_{i}
\right)$, is also studied. For that purpose, a model $(
\tilde{\mathcal{K}},\tilde{A},\tilde{\Gamma } )$ to represent $Q:=Q_{1}+Q_{2}$
in terms of $\left( \mathcal{K}_{i},A_{i},\Gamma_{i} \right)$ is created. By
means of that model, necessary and sufficient conditions for $\kappa
=\kappa_{1}+\kappa_{2}$ are proven in analytic terms. At the end, it is
explained how degenerate Jordan chains of the representing relation $A$ affect
reducing subspaces of $A$ and decomposition of the corresponding function $Q$.
