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Abstract By decomposing functions, we establish some boundedness results for some rough singular integrals on the homogeneous Morrey-Herz spaces M K ˙ q , p ( ⋅ ) α ( ⋅ ) , λ ( R n ) $M\dot{K}_{q, p(\cdot)}^{\alpha(\cdot),\lambda}({\Bbb{ R}}^{n})$ , where the two main indices are variable. The corresponding results as regards their commutators are also considered.