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In this paper, we introduce the concept of monochromatic kernel-perfect digraph, and we prove the following two results: (1) If D is a digraph without monochromatic directed cycles, then D and each ${\alpha }_v,v\in V\left(D\right)$ are monochromatic kernel-perfect digraphs if and only if the composition over D of ${\left({\alpha }_v\right)}_{v\in V\left(D\right)}$ is a monochromatic kernel-perfect digraph. (2) D is a monochromatic kernel-perfect digraph if and only if for any B ⊆ V(D), the duplication of D over B, $D^B$, is a monochromatic kernel-perfect digraph.