A novel technique is presented for estimating white matter connectivity in vivo using diffusion-weighted magnetic resonance imaging. The concept of a fibre orientation density function (ODF) is described, which characterises the uncertainty in the orientation of the underlying white matter fibres, given the set of diffusion-weighted signal intensities at the point of interest. The proposed algorithm is based on the evolution of a front from a seed region, using the information provided by the fibre ODF. Each point reached by the front is assigned an index of connectivity with the seed region. The algorithm was used to track various major white matter fibre pathways in two data sets acquired on the same healthy adult volunteer over separate occasions. Example tracks are shown to illustrate some of the properties of the algorithm, such as robustness to noise and branching capability. Finally, the dependence of the algorithm on the model used to derive the fibre ODF is discussed.