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In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ→N/Γ be a covering map of a nil-manifold and denote by A:N/Γ→N/Γ the nil-endomorphism which is homotopic to f.If f is a special TA-map,then A is a hyperbolic nil-endomorphism and f is topologically conjugate to A.