Summary: The \(m\)-order commutator \(T^m_b\) is generated by a function \(b\in BMO (\mathbb{R}^n)\) and strongly singular integrals operator \(T\). The bounded result of \(T^m_b\) is already existed in \(L^q (\mathbb{R}^n)\) space. Based on the inequality technique, the boundedness of \(T^m_b\) in Herz spaces and Morrey-Herz spaces has been further studied respectively. The results are proved to be general.