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This study highlighted the occurrence of a pelagic long line fishery targeting albacore tuna, yellowfin tuna and bigeye tuna in the high seas of eastern Pacific Ocean. Species selectivity of the fishing method was assessed. Hook depth, statistics of at-vessel survival rate grouped by hooks number, length frequency, weight frequency, length weight relationship, relative condition factor and Fulton’s condition factor were estimated for the target species. This fishing method proved highly selective for albacore tuna, where catches accounted for about 85% of catches, while other resources such as yellowfin tuna amounted to 4.8% and big eye tuna accounted for 9.70%. The results showed that, fish size increased with deeper depths. Hook No. 8 located at a critical depth indicated that fork lengths of tuna registered above this depth were significantly smaller than that those captured below it. Logistic regression model suggested a significant effect of hook depth on the catch efficiency. The highest density of catch efficiency was located at the depth of 167.57 m. An alternative strategy showed that hooks deployed at the depths ranging from 124 to 211 m will result in a more considerable fishing efficiency. The analyses also showed that the relative condition factors (Krel) of the three fish species were greater than (1) implying that they were in good physiological condition at the time of capture.