Composite polymer nanofibers containing single-walled carbon nanotubes (SWCNT) are fabricated by electrospinning. We describe the path from dispersing individual SWCNTs or thin bundles in water using amphiphilic polymers, through a structural characterization of the polymer conformation in the SWCNT/polymer hybrid to the characteristics of the electrospun composite nanofibers. An alternating copolymer of styrene and sodium maleate (PSSty) and gum arabic (GA)-a highly branched natural polysaccharide were successfully used to produce stable aqueous dispersions. Measurements of small angle neutron scattering (SANS) show that both polymers form a thick corona of adsorbed coils on the nanotubes, resulting in a thick cylindrical hybrid. The large coils introduce a significant steric barrier stabilizing the dispersions, in addition to electrostatic repulsion by charged groups. The composite nanofibers showed good distribution and alignment of the SWCNTs in the poly(ethylene oxide) (PEO) matrix. Enhanced tensile properties were achieved due to a high degree of alignment of both nanotubes and PEO crystals, and a strong interface, especially with PSSty.