The dispersal of Glossina species is of interest to pest control personnel since these flies are the biological vectors of human and animal trypanosomes in Africa. The design of control and/or eradication programmes requires an accurate knowledge of the ecological characteristics of tsetse flies and the geographic structure of their populations. The present study attempts to model the dispersal process of a riverine tsetse species, i.e. Glossina palpalis gambiensis Vanderplank in Burkina Faso along an apparent homogeneous gallery forest. While for savannah species, dispersal is usually modelled as a two-dimensional random walk (in time and space) or diffusion (its continuous analogue), for riverine species, dispersal can be viewed more simply as a one-dimensional random walk. The data reported here show that the topology of the habitat, which is a system of tributaries rather than a straight line, has a great impact on the dispersal process. Moreover, since only a part of the river system can be observed in practice, the effect of partial observation when estimating dispersal parameters can be quantified. The results reported here were obtained using a data set from a mark-release-recapture experiment carried out with G. p. gambiensis on a tributary of the Mouhoun River in Burkina Faso. The model was fitted to field data and used to estimate the displacement of a fly during 10% of its lifespan (13 kilometres) and the probability of it dispersing more than 10 kilometres from its initial position (P > 0.1). The analysis was carried out by either taking into account, or ignoring, the fact that only part of the river system was observed during the mark-release-recapture protocol.