Polymer based graphene nanocomposites have been extensively investigated to develop conductive materials using classical polymer processing techniques, for various applications including optoelectronic, energy storage, EMI shielding among others. The challenge in the design of those materials relies in a proper control of their microstructure with a conductive path of graphene nanoparticles at a concentration, known as percolation threshold, as low as possible. One possibility to reduce this concentration consists of using multiphase polymer matrices such as immiscible polymer blends. In this case, the distribution and shape of the different polymer phases, or blend morphology, together with the chemical affinity between the components will help defining the location and orientation of the nanoparticles. In this work, graphene nanoplatelets (GN) produced by mechano-chemical exfoliation of graphite were incorporated in LLDPE/EVA blends of different concentration by melt mixing, to obtain conductive composites. The processing parameters and sequence of materials feeding were optimized to reduce the percolation threshold. The stability of the morphology and electrical properties of the obtained materials during annealing after processing were also was addressed. The experimental results showed that the feeding sequence and annealing affected greatly the percolation threshold and that the addition of graphene resulted in a refinement of the blends morphology. Small amplitude oscillatory shear tests, together with rheological models were then used to get an understanding of the role of graphene as a conductive filler and morphology modifier. Time sweep shear tests were used to evaluate the evolution of the morphology, induced by diffusion of graphene during annealing.