Interspecific competition between individuals of different species can result in reductions in their fecundity, growth or survival, reflecting differential exploitation of resources that become intensified due to spatial co‐occurrence, ecological similarity and increased population densities. As two species cannot occupy the same niche, coexistence is only possible if the available resources are used in non‐overlapping manners such as niche partitioning or the use of refuges. Among agricultural insect pests, such as fruit flies of the family Tephritidae, competitive interactions can result in competitive displacement, host changes, or the expansion or restriction of the numbers of hosts utilized that can have negative consequences for human agricultural activities. We evaluated the competitive interactions between two fruit fly species of the genus Anastrepha, Anastrepha obliqua (Macquart, 1835) and Anastrepha fraterculus (Wiedmann, 1830), on their respective preferred hosts (mangoes and guava). Experiments of larval competition and competition for ovipositioning sites by adult females were performed to compare the parameters of larval development time, numbers of pupae and emerged adults and numbers of ovipositions in the presence or absence of interspecific competition. We observed that the interactions between those species were asymmetrical and hierarchical, and our results suggest a competitive displacement of A. fraterculus by A. obliqua when those two species are present on the same fruit, whether mangoes or guavas.