Electrospinning has been used to produce porous, low density, polymer–nanotube composite membranes. The membrane mechanical properties can be enhanced by tuning the nanotube content, aligning the fibers during spinning, and by post production drawing. The mechanical properties are maximized for membranes with a nanotube content of 0.43 vol %. Aligned composites at this volume fraction have been prepared by spinning onto a rotating drum collector electrode. This method results in significant increases in modulus, strength, and toughness. The best composites, produced at the maximum drum rotation rate, were post treated by a drawing step to result in further increases in modulus and strength. These methods allows the production of membranes with densities as low as ∼340 kg m−3 but with values of stiffness, strengths and toughness's more typically found in bulk thermoplastics; 1.2 GPa, 40 MPa, and 13 J g−1.