Single-walled carbon nanotubes (SWNTs) are pi-conjugated, quasi-one-dimensional structures consisting of rolled-up graphene sheets that, depending on their chirality, behave as semiconductors or metals1; owing to their unique properties, they enable groundbreaking applications in mechanics, nanoelectronics and photonics2, 3. In semiconducting SWNTs, medium-sized excitons (3–5 nm) with large binding energy and oscillator strength are the fundamental excitations4, 5, 6, 7, 8; exciton wavefunction localization and one-dimensionality give rise to a strong electron–phonon coupling9, 10, 11, the study of which is crucial for the understanding of their electronic and optical properties. Here we report on the use of resonant sub-10-fs visible pulses12 to generate and detect, in the time domain, coherent phonons in SWNT ensembles. We observe vibrational wavepackets for the radial breathing mode (RBM) and the G mode, and in particular their anharmonic coupling, resulting in a frequency modulation of the G mode by the RBM. Quantum-chemical modelling13 shows that this effect is due to a corrugation of the SWNT surface on photoexcitation, leading to a coupling between longitudinal and radial vibrations.