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Highlights • Data for control strategies of Bactrocera oleae in places at risk of invasion. • There is presence potential of B. oleae on South America and Oceania. • Fopius arisanus presented a greater potential of geographic distribution. • Psyttalia concolor was highlighted in areas related to the olive tree crop. Abstract Bactrocera oleae (Rossi, 1790) (Diptera: Tephritidae) is monophagous and one of the primary plagues of the olive tree (Olea europaea L. (Lamiales: Oleaceae)), causing economic losses worldwide. The pest has been detected in the United States and Mexico, showing potential to invade new areas. Among the parasitoids used to control B. oleae , Fopius arisanus (Sonan, 1932) and Psyttalia concolor (Szépligeti, 1910) (Hymenoptera: Braconidae) are considered cenobiont and sinovigene endoparasitoids. Through the study of the potential geographic distributions, the size of regions environmentally suitable for the species can be understood, and the areas of distribution of the pest can be related with those of the parasitoids, with the goal to estimate whether the parasitoids would be suitable for use in classic biological control. The aim of this study was to map the potential global distribution regions, with an emphasis on South America, of B. oleae and the two parasitoids F. arisanus and P. concolor and show the overlap of geographically environmentally adequate areas for the joint establishment of the pest and natural enemy. For map the potential global distribution regions, a predictive model correlative of the distribution of the species was used, generated from known data of the localities of occurrence of insects and environmental predictor variables. The algorithm chosen for the modeling was Max Entropy (MaxEnt). The evaluation of the model was based on the mean Area Under the Curve (AUC), which was 0.966, 0.982 and 0.995 for B. oleae , F. arisanus , and P. concolor , respectively, indicating good predictive performance of the models and reliable projections. In general, the most significant extent of the potential distribution of F. arisanus was observed in Asia (most likely because it is the region of origin), Central America and South America. In Africa and North America, F. arisanus was also the most comprehensively distributed, in general; however, in the regions related to the occurrence of B. oleae and olive cultivation, P. concolor presented a greater potential distribution than that of F. arisanus. In Europe and Oceania, P. concolor had potential distribution projected in areas with olive groves. [ABSTRACT FROM AUTHOR]