Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/1752 2022 2022 Sudan University of Science and Technology, Faculty of Science, Khartoum, Sudan Othman Al Al-basheer In this paper we generalize the concept of 2-quasi -- nuclear operators between Normed spaces to -quasi--nuclear operators between locally convex spaces and we study the relationship between p-quasi-- nuclear, nuclear operators, -nuclear, quasi-nuclear and quasi-- nuclear. Also, we prove that the composition of two operators, one of them is a -quasi--nuclear, is again a p-quasi--nuclear operator. 2023 2023 12 16 10.54216/GJMSA.050202 https://www.americaspg.com/articleinfo/33/show/1752