Animals may anticipate and try to avoid, at some costs, physical encounters with other competitors. This may ultimately impact their foraging distribution and intake rates. Such cryptic interference competition is difficult to measure in the field, and extremely little is known at the interspecific level. We tested the hypothesis that smaller species avoid larger ones because of potential costs of interference competition and hence expected them to segregate from larger competitors at the scale of a resource patch. We assessed fine-scale spatial segregation patterns between three African herbivore species (zebra Equus quagga, kudu Tragelaphus strepsiceros and giraffe Giraffa camelopardalis) and a megaherbivore, the African elephant Loxodonta africana, at the scale of water resource patches in the semi-arid ecosystem of Hwange National Park, Zimbabwe. Nine waterholes were monitored every two weeks during the dry season of a drought year, and observational scans of the spatial distribution of all herbivores were performed every 15 min. We developed a methodological approach to analyse such fine-scale spatial data. Elephants increasingly used waterholes as the dry season progressed, as did the probability of co-occurrence and agonistic interaction with elephants for the three study species. All three species segregated from elephants at the beginning of the dry season, suggesting a spatial avoidance of elephants and the existence of costs of being close to them. However, contrarily to our expectations, herbivores did not segregate from elephants the rest of the dry season but tended to increasingly aggregate with elephants as the dry season progressed. We discuss these surprising results and the existence of a trade-off between avoidance of interspecific interference competition and other potential factors such as access to quality water, which may have relative associated costs that change with the time of the year.