Single-wall carbon nanotubes (SWNTs) with anionic or cationic coatings have been prepared by exploiting the ability of certain surfactants to form a monolayer shell around the nanotube. The presence of electrically charged functional groups on the surface of the SWNT allows thin film deposition to proceed via the electrostatic layer-by-layer method. This self-assembly process was monitored using the quartz microbalance technique and Raman spectroscopy, while the morphology of the resulting thin layers was studied with atomic force microscopy. A variety of different architectures has been built up. In one arrangement, a single species of a modified SWNT (anionic or cationic) was alternated with a passive polymer to form a composite structure. A 'superlattice' architecture comprising alternating anionic and cationic modified nanotubes was also fabricated. The in-plane and out-of-plane dc conductivities of the films were measured at room temperature and contrasted with reference architectures (i.e. those containing no nanotubes). The results showed clearly that the incorporation of SWNTs into the multilayer assemblies provided electrically conductive thin films. It is suggested that the current versus voltage behaviour, particularly in the out-of-plane direction, is controlled by quantum mechanical tunnelling of carriers between the nanotubes.