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This paper aims to address current limitations of 3D printed conductive materials through the development of a novel formulation of a thermoplastic composite. In particular, a conductive filament suitable for three-dimensional printing is obtained on the basis of Polylactic acid (PLA) filled with two types of highly conductive nano-carbon materials, i.e. multi-walled carbon nanotubes (MWCNTs), graphene nanoplates (GNPs) and a combination of both fillers (MWCNT/GNP). A systematic rheological and electrical characterization of the resulting nanocomposites is presented. Viscoelastic properties and rheological percolation threshold are determined for the binary and ternary composites and related to the size of nanoparticles. Comparable values for the percolation threshold are found by means of rheological and electrical studies. Low electrical percolation thresholds and high values of the electrical conductivity of the order of S/m are achieved for the investigated formulations. At the highest filler loading (i.e. 12 wt%) the electrical conductivity reaches the value of 4.54 S/m, 6.27 S/m and 0.95 S/m for the composites based on MWCNTs, GNPs and multiphase system, respectively. These results, together with the good stability shown by the nano-reinforced PLA in the frequency range [100 Hz-1MHz] make these composites promising candidates for 3D printed conductive devices for electromagnetic (EM) applications.