Two of the main types of nanotubular architectures are the single-walled carbon nanotubes (SWCNTs) and the self-assembling cyclic peptide nanotubes (SCPNs). We here report the preparation of the dual composite resulting from the ordered combination of both tubular motifs. In the resulting architecture, the SWCNTs can act as templates for the assembly of SCPNs that engage the carbon nanotubes noncovalently via pyrene "paddles", each member of the resulting hybrid stabilizing the other in aqueous solution. The particular hybrids obtained in the present study formed highly ordered oriented arrays and display complementary properties such as electrical conductivity. Furthermore, a self-sorting of the cyclic peptides toward semiconducting rather than metallic SWCNTs is also observed in the aqueous dispersions. It is envisaged that a broad range of exploitable properties may be achieved and/or controlled by varying the cyclic peptide components of similar SWCNT/SCPN hybrids.