The effective dielectric response of composites containing anisotropic graded cylindrical inclusions whose graded profile along the radial direction is different from that along the tangential direction in cylindrical coordinates, has been investigated. As an example, we have studied composites of anisotropic graded cylindrical inclusions with general power-law profiles, [Formula: see text] and [Formula: see text], where r is the distance of a point in the cylindrical inclusion from the origin. Analytical solutions of the local electric potentials are derived in terms of the hyper-geometric function and the formulas for calculating the effective response of anisotropic graded composites are given in the dilute limit. Furthermore, we have validated the anisotropic differential effective dipole approximation (ADEDA) by comparing with our exact results, and obtained excellent agreement.