DNA nanotubes are an attractive class of materials that can be assembled with precise control over their size, shape, length and porosity, and can encapsulate and release materials in response to specific added molecules. In parallel, block copolymer assemblies can provide biocompatibility, stability, nuclease resistance, the ability to encapsulate small molecules, long-range assembly and numerous additional functionalities that can be tuned with subtle chemical modifications. Herein, we describe a new class of hybrid materials in which block copolymer assemblies are sequence-specifically and longitudinally positioned on robust DNA nanotubes constructed using rolling circle amplification. These materials are dynamic, allowing the polymer structures to be cleanly removed from the DNA nanotubes only when a specific DNA sequence is added, and creating a single-stranded form of these nanotubes. Specifically, we first describe the use of rolling circle amplification to create a long DNA strand containing a repeat sequence. This is used as a guide strand in a new method to construct robust nanotubes with a non-nicked backbone. We then synthesize polymer–DNA conjugates through on-column functionalization of a DNA strand with a polymer. These conjugates self-assemble into spherical aggregates, which then position themselves onto the DNA nanotubes using sequence-specific hybridization, creating a ‘striped' structure. The polymer aggregates can be cleanly lifted off the nanotubes using a strand displacement strategy, thus uncapping these DNA nanotubes. We also show that this longitudinal alignment of polymer aggregates on DNA nanotubes is general for a variety of DNA–block copolymers.