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We study the generalization of S-duality for **4d N=2** superconformal gauge theories involving Argyres-Douglas type SCFT as their constituents. The Argyres-Douglas theories are **4d N=2** SCFT with Coulomb branch operators of fractional scaling dimensions, which often have a non-abelian flavor symmetry. We gauge the flavor symmetry together with additional hypermultiplets so that the gauging is exactly marginal. At the strong coupling limit of the gauge coupling, we have a different weak coupling description of the same theory. We will particularly discuss the cases in which the gauge group is **SU(2)** or **SU(3)**. These are analogues of S-duality in the **SU(2)** gauge theory with 4 flavors or the **SU(3)** gauge theory with 6 flavors, whose matter sectors are now replaced by Argyres-Douglas theories.

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