Fibers produced by melt spinning of conductive polymer composites are attractive for several applications; the main drawback is however reduced processability at high filler concentrations. Carbon nanotubes (CNTs) are considered suitable fillers for conductive polymer composites, replacing conductive grades of carbon black (CB). In this study, the fiber-forming properties of conductive polymer composites based on a conductive grade of CB and two masterbatches with CNT in a polyethylene matrix were investigated. The CB was also used in a polypropylene matrix for comparison. The rheological properties of the filler-containing melts in shear and their extensional behavior were evaluated. A piston-driven device was used to extrude the molten materials through a capillary; different capillary geometries were tested. Fibers were produced at various draw ratios, and their conductivity was determined. To assess the ultimate extensibility, a modified Rheotens method was used. The results showed that a conductive CB grade can have a lower percolation threshold and higher conductivity than a material with CNT. Conductivity decreased with increasing melt draw ratio for both types of fillers. The spinnability of the materials decreased with increasing concentration of filler material and correlations were found between spinnability and melt elasticity.