Styrenic thermoplastic elastomers such as Poly[styrene-b-(ethylene-co-butylene)-b-styrene] (SEBS) constitute a special class of block copolymers composed of two styrene endblocks and a soft rubber midblock. Due to their immiscibility, the blocks self-assemble into well-ordered nanostructured morphologies that depend on several parameters such as their molecular weights, affinities and relative fractions. These organized morphologies have great potential to act as templates tailoring the dispersion and spatial distribution of nanoparticles with different shapes in order to achieve well designed nanocomposites with optimized functional properties. In this study, both Zinc Oxide (ZnO) nanospheres and exfoliated hexagonal boron nitride (h-BN) have been dispersed in SEBS grafted maleic anhydride (SEBS-MA) triblock copolymer in a trial to achieve thermally conductive electrically insulating nanocomposites, that benefit from potential synergetic effect of both nanoparticles. SEBS-MA/ZnO nanocomposites, studied beforehand, featured an interesting rheological behavior, even at low loading of ZnO, characterized by a consistent increase of dynamic moduli and reduced dependence on the frequency especially in the low values range indicating the formation of networks between ZnO nanoparticles and polymer chains. Moreover, improvements of breakdown strength, thermal conductivity and resistance to surface erosion were achieved. In a second step, h-BN particles were partially exfoliated and dispersed in SEBS-MA/ZnO mixture by means of high-shear mixing. The dispersion of these anisotropic fillers in the hybrid nanocomposite was enhanced compared to direct dispersion in neat SEBS-MA. The impact of this combination on the dielectric performance was investigated through the evaluation of the complex dielectric permittivity, breakdown strength and thermal conductivity in correlation with the rheological properties. Key words: block copolymer nanocomposite, tailored dispersion, network, dielectric properties...