The fly-round has for long been regarded as the most satisfactory way of following fluctuations in populations of tsetse flies (Glossina) and locating areas of concentration. It consists of a path cut through bush so as to traverse the principal vegetation communities and is divided into sections, corresponding to the latter, on each of which the flies are caught. A modification now widely used but not previously described in detail is termed a line transect or transect fly-round; this follows an arbitrary course along straight lines that may be orientated with regard to the topography and is divided into numerous short sections of equal length terminating at posts at which flies are caught. In its simplest form it follows a straight course, but various patterns are used including an angular spiral. It facilitates the collection of quantitative data on tsetse density and the factors (such as vegetation) that affect it, and their analysis is possible in more detail than was the case when the fly-round was laid out according to a pre conceived notion of vegetational relationships. This is illustrated by data from a fly-round at Shinyanga, Tanganyika, consisting of six sides, each of 2,000 yd., of two diagonally adjoining squares, that was divided originally into nine sections of varying lengths representing the floristic communities traversed, and subse quently into 120 sections each 200 yd. long. Comparison of the catches of non-teneral males of G. swynnertoni Aust. grouped according to the two methods emphasises the much greater detail provided by the second of them. The transect fly-round is easy to lay out and operate and is thought likely to be particularly useful in connection with reclamation work.The effect of varying the section length was investigated for G. swynnertoni at Shinyanga, G. pallidipes Aust. in Nyanza Province, Kenya, and G. austeni Newst. in Zanzibar. With the first, progressively fewer flies of all categories except teneral males were caught as the section length was increased progressively from 50 to 200 yd.; with the other species a similar tendency was apparent, but not significant. The results emphasise a point long recognised but often neglected, that data from fly-rounds reflect, in part, the reaction of tsetse populations to the behaviour of the catching party. That this reaction, termed the availability, is itself inconstant is shown by catches of G. pallidipes on a fly-round done daily for a month, in which differences between catches on consecutive days, sometimes exceeding 3:1, must represent changes in availability, not in absolute population.Data from the transect fly-round can be analysed so as to indicate sections where the catches deviate significantly from those expected on the assumption that they are distributed according to a Poisson series, and where there may thus be presumed to be areas of concentration of the population, or the reverse. A Table is provided to facilitate such analysis.