We present a simple and general model that describes the ordered assembly of polymer strands on nanotube surfaces. Energetically favorable coiling angles are identified based on geometric constraints that limit the maximum coverage of polymers on the walls of the nanotubes. The coiling angles can be controlled by selecting the appropriate nanotube diameters, opening the possibility of engineering the strength of composite fibers. The model is applied to two different polymeric molecules; namely, polyacetylene and a polyphenylenevinylene derivative. (C) 2004 American Institute of Physics.