Since 1995, bluefin tuna (Thunnus thynnus) have been caught by purse seine in order to place the live fish in floating cages, feed them during various months with fish and pelagic cephalopods and later kill them for shipment mainly to the Japanese market. As a result of this practice, the natural stocks of this species are in an overfished state and therefore it has been necessary to implement catch limits (TACs). Since the tunas cannot be manipulated at the time of their capture, the estimate of the biomass of tunas caught must be carried out by visual methods using video cameras that are placed at the time when the tunas are transferred from the purse seine net to the towing cage. Therefore, there are no direct data on the catch until the animals are killed some months later, when evidently there is a variation in their weight. On the other hand, the regulation of the fishery requires immediate knowledge of the catch in order to close the fishery when the quota has been reached. This paper proposes the development of a system that permits estimating the number and the biomass of bluefin tunas by acoustic means, both at the time of transfer as well as during their fattening in the floating cages.