For the last few years poly(styrene-b-ethylene-co-butylene-b-styrene)/multi-walled carbon nanotubes (SEBS/MWCNT) nanocomposites have gained attention as these materials can present interesting properties, and be used in different applications, such as antistatic coating, EMI shielding, temperature sensor, artificial muscle, flame retardant, etc. MWCNT have remarkable electrical, thermal and mechanical properties, and the block copolymer (SEBS) can provide a template to tailor the morphology and therefore the engineering properties of the nanocomposites. In this work, SEBS/MWCNT nanocomposites with different concentrations of MWCNT were obtained by melt mixing in a twin-screw extruder. The morphology was characterized using small amplitude oscillatory shear (SAOS) and small angle X-ray Scattering (SAXS). The electrical and dielectric properties of the samples were also evaluated. Rheological and SAXS results indicated that SEBS block copolymers presented a morphology of PS cylinders within a EB matrix. The state of dispersion of CNT was accessed using SAOS measurements. Different methodologies were applied to investigate the rheological and electrical percolation threshold, for example, power law theory, Van-Gurp Plot, etc. A low rheological percolation threshold was achieved. When only 0.25wt% of CNT was added to SEBS, the slope changed of G’=f(0.1-0.01) from 0.29 to 0.05. The electrical percolation threshold was achieved at lower concentration than 1.00wt% of CNT: when 1.00 wt% of CNT was added to SEBS, the composite became electrically conductive.