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Let L be the set of all hereditary and additive properties of graphs. For P₁, P₂ ∈ L, the reducible property R = P₁∘P₂ is defined as follows: G ∈ R if and only if there is a partition V(G) = V₁∪ V₂ of the vertex set of G such that $⟨V₁{⟩}_G\in P₁$ and $⟨V₂{⟩}_G\in P₂$. The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the decomposition of a reducible property into irreducible ones.