Structures of carbon nanotube/ligand complexes were studied by flow linear dichroism (the differential absorption of light polarized parallel and perpendicular to the flow orientation direction) with the aim of establishing linear dichroism as a technique to study such systems. Anthracene, naphthalene, and DNA were chosen as ligands, and the potential for flow linear dichroism to probe ligands noncovalently (as well as covalently) bound to single-walled nanotubes is reported. Linear dichroism enables the determination of approximate orientations of the ligands on the carbon nanotubes.