Free-flying wild tsetse flies (Glossina pallidipes Aust. and G.m. morsitans Westw.) were video recorded in Zimbabwe as they flew within an artificial host odour plume at 3, 7 or 15 m from the source, or in no odour, with and without a 0.75 m2 vertical, black visual target present aligned with the wind. With no visual target present, flights in odour were strongly biased upwind, and in the absence of odour strongly biased downwind. With the target present, between 16% and 40% of the upwind approaching flies responded visually as they passed the target, by circling it, in proportion to the proximity of the source (taken to be proportional to the mean odour concentration). Crosswind approaching flies (for whom the target will have been visible for some metres away) circled more frequently (34-56%), but without obvious correlation with the odour concentration. Circling flies also responded orthokinetically, by slowing down as they passed the target. The departure directions relative to the wind of flies leaving the target were significantly affected by the odour concentration. At 3 m they left the target in all directions, except possibly avoiding due upwind. At 7 m they left with an obliquely upwind bias, but at 15 m and also in no odour, they left with a strong crosswind bias.