Exporatory fishing with bottom trawl conducted by the French trawler « Austral» off the Crozet archipelago (sub-area 58-6) does not allow to detect any other marine living resources than the only one Nototheniid fish Dissostichus eleginoides. The other species have no future for a commercial exploitation due to their sizes. Deep-sea fishing only (slope of the shelf :300 - 750 m) show some shoals of sub-adults and adults as observed in the division 58-5-1 (Kerguelen) located more easternly. Two geographical areas have been specially identified. Trends in yield are however not stable from one year to another and even along one fishing experiment despite a limited fishing effort. Two hypothesis are proposed to explain the trends: a quick col1apse or/and a high migratory pattern of this part of the stock. The running experiments do not allow to consider and work out a plan an high fishing effort (or in the future and even yearly fishing cruises in the sub-area.