Unmanned Aerial Systems (UAS) are increasingly being used recreationally, commercially and for wildlife research, but very few studies have quantified terrestrial mammalian reactions to UAS approaches. We used two Vertical Take-off and Landing (VTOL) UAS to approach seven herbivore species in the Moremi Game Reserve, Botswana, after securing the relevant permissions. We recorded responses to 103 vertical and 120 horizontal approaches, the latter from three altitudes above ground level (AGL). We ran mixed logistic regressions to identify factors triggering (i) any response and (ii) an evasive response. We included effects of activity, altitude, direction of approach, distance, habitat, herd type, herd size, other species, target species, time, VTOL type and wind strength. Response triggers were linked to altitude, distance, habitat and target species. Elephant (Loxodonta africana), giraffe (Giraffa camelopardalis), wildebeest (Connochaetes taurinus) and zebra (Equus quagga) were most affected by VTOL approach, impala (Aepyceros melampus) and lechwe (Kobus leche) were least responsive, and tsessebe (Damaliscus lunatus) displayed intermediate sensitivity. VTOLs flown lower than 60 m AGL and closer than 100 m horizontal distance from target animals triggered behavioural responses in most species. Enforced regulations on recreational UAS use in wildlife areas are necessary to minimise disturbance to terrestrial mammals.