Self-assembled nanotubular structures have numerous potential applications but these are limited by a lack of control over size and functionality. Controlling these features at the molecular level may allow realization of the potential of such structures. Here we report a new generation of self-assembled cyclic peptide–polymer nanotubes with dual functionality in the form of either a Janus or mixed polymeric corona. A ‘relay’ synthetic strategy is used to prepare nanotubes with a demixing or mixing polymeric corona. Nanotube structure is assessed in solution using 1H–1H nuclear Overhauser effect spectroscopy NMR, and in bulk using differential scanning calorimetry. The Janus nanotubes form artificial pores in model phospholipid bilayers. These molecules provide a viable pathway for the development of intriguing nanotubular structures with dual functionality via a demixing or a mixing polymeric corona and may provide new avenues for the creation of synthetic transmembrane protein channel mimics.