Distributions of the specific energy deposited in nanometre-sized volumes have been measured as a function of the radial distance from the path of 5.9 MeV.amu-1 uranium and 13.0 to 17.2 MeV.amu-1 germanium beams. Tissue volumes of 125, 250, 500 and 1000 nm diameter were simulated using a grid-walled proportional counter capable of two-dimensional motion relative to the ion beam. Radial distances from 0 to 8000 nm were investigated. Values of the mean specific energy were obtained from these distributions and compared with radial dose profiles calculated from track structure models. Excellent agreement was observed between the measured mean specific energy and the calculated radial dose for small distances relative to the track path. At longer distances, the mean specific energy deposited in small volumes became larger than the calculated average dose, reflecting the stochastic nature of the energy deposition process, i.e. at greater distances from the ion path a small site was either hit, by the traversal of secondary electron or absorption of a photon, or received no energy. If one accounts for the fraction of the particles that deposit no energy in the site, then the average specific energy deposition per particle is in excellent agreement with model calculations.