The incorporation of carbon nanotubes to thermoplastic fibers can potentially improve mechanical, thermal and electrical properties. In this article, a methodology to tailor the mechanical properties of carbon nanotube/nylon fibers is presented. Multiwalled nanotubes (MWNT) were combined to polyamide 12 through melt compounding and twin-screw extrusion. Pellets containing between 0 and 5.0 wt % MWNT were extruded and subsequently melt spun with a capillary rheometer to produce filaments. To further promote the alignment of the polymer chains and MWNTs, postdrawing parameters were systematically investigated: temperature, drawing speed and elongation. The best improvements in terms of elastic modulus and yield strength were measured at 140 C and 500% elongation, whereas drawing speed was shown to have a negligible effect. It was confirmed through electron microscopy and X-ray diffraction that these enhancements were mainly induced by the alignment of the polymer chains along the fibers' axis.