A direct numerical technique has been used to investigate the kinetics of impurity precipitation on dislocations making full allowance for diffusion and with a strong elastic interaction between the solute atoms and the dislocations. A distinction is made between the growth of discrete precipitate particles and continuous rod-like precipitates on the dislocations. The kinetics for the former mode of precipitation are obtained for various values of a constant transfer velocity across the precipitate matrix interface; it is found that the fraction of solute remaining in free solution decreases exponentially with time. The continuous rod-like mode of precipitation is a consequence of a relatively high binding energy in the dislocation core, and it is shown that such a situation should lead to a transient variation of the transfer velocity across the matrix-core interface. Under these conditions, the kinetics of precipitation closely resemble the experimentally determined strain ageing kinetics in some low-carbon and nitrogen steels.