The feeding behaviour of small tuna on the mesopelagic fish Vinciguerria nimbaria was studied in an equatorial area of the Atlantic Ocean (10–20° W, 0–5° N). Acoustic data (from a scientific cruise) and tuna stomach content data (from the tuna purse-seine fishery) were combined. V. nimbaria formed loose schools that occurred in clusters during daytime, and large aggregations during the night. The characteristics of the schools and clusters were analysed. The average length, size and packing density of the day-school were estimated at 48.5 m, 24400 individuals, and 5.8 fish m–3, respectively. The average length of clusters was close to 10 km. The packing density of night-school was estimated at 1.6 fish m–3. The preying of tuna on V. nimbaria was modelled as a stochastic process based on two Poisson processes. Daily rations of tuna were estimated at 3.5% and 7% of the body weight. Taking into account the swimming performance of the prey and the predator, we showed that tuna were able to feed on day-schools in a very short time, whereas feeding during the night by filtering was not competitive. Furthermore, a cluster is able to feed a single tuna school during 2 months, proving the sustainability of the biomass of small tuna in the area by V. nimbaria.