A simple method was used to assemble single-walled carbon nanotubes into indefinitely long ribbons and fibers. The processing consists of dispersing the nanotubes in surfactant solutions, recondensing the nanotubes in the flow of a polymer solution to form a nanotube mesh, and then collating this mesh to a nanotube fiber. Flow-induced alignment may lead to a preferential orientation of the nanotubes in the mesh that has the form of a ribbon. Unlike classical carbon fibers, the nanotube fibers can be strongly bent without breaking. Their obtained elastic modulus is 10 times higher than the modulus of high-quality bucky paper.