This article applies the Rapfish methodology, a non-parametric and multi-disciplinary technique, with the objective of defining and evaluating a Sustainability Index of the Basque purse-seine fleet, fishing tropical tuna in the Indian and Atlantic Oceans. The estimated Sustainability Index for the fleet fishing in the Indian Ocean is above a critical sustainability treshold and improves between 1998 and 2009. The opposite occurs for the fleet in the Atlantic Ocean. The influence of the growing use os Fish Aggregating Devices on the behaviour of fishers in the Indian Ocean is also analysed.