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The boundedness of the iterated maximal operator $M^2$ from $\\mathcal{M}_{L(\\log L),\\lambda}$ to weak Zygmund-Morrey space ${\\mathcal {W \\! M}}_{L(\\log L),\\lambda}$ is proved. The class of functions for which the maximal commutator $C_b$ is bounded from $\\mathcal{M}_{L(\\log L),\\lambda}$ to ${\\mathcal {W \\! M}}_{L(\\log L),\\lambda}$ are characterized. 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The boundedness of the iterated maximal operator $M^2$ from $\\mathcal{M}_{L(\\log L),\\lambda}$ to weak Zygmund-Morrey space ${\\mathcal {W \\! M}}_{L(\\log L),\\lambda}$ is proved. The class of functions for which the maximal commutator $C_b$ is bounded from $\\mathcal{M}_{L(\\log L),\\lambda}$ to ${\\mathcal {W \\! M}}_{L(\\log L),\\lambda}$ are characterized. 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