Estimates of the intrinsic lifetime of low-frequency zone-centre phonon modes in silicon nanowires and carbon nanotubes have been presented from the application of Fermi's golden rule formula based upon an elastic continuum model for cubic anharmonicity. In particular, results have been presented for the lowest non-zero mode in both nanostructures, and also the breathing mode in the nanotube. Except for the ultrathin nanowire, the lifetime increases with size and decreases with an increase in temperature. Typically, these modes have a lifetime of the order of nanoseconds, almost a thousand times larger than the lifetimes of optical phonon modes in the corresponding bulk materials. Also, at room temperature the lifetime of the lowest non-zero mode is nearly an order of magnitude larger in the (20,20) nanotube than in the nanowire of similar thickness (width 2.2 nm). (c) 2006 Elsevier B.V. All rights reserved.