International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1056 2020 2020 Al-Imam Al-Kadhum College For Islamic Science University, Iraq Basheer Abd Al Rida Sadi This paper is dedicated to study the group of units problem in some 2-cyclic refined neutrosophic rings, where it presents a full classification of the group of units in 2-cyclic refined neutrosophic ring of integers  , 2-cyclic refined neutrosophic ring of integers modulo 2 and 3 ,  and 2-cyclic refined neutrosophic ring of real numbers , as direct products of the cyclic groups. On the other hand, this work provides a necessary and sufficient condition for the invertibility of any square 2-cyclic refined neutrosophic real matrix. Also, we will illustrate some examples to clarify the validity of our work. 2022 2022 48 58 10.54216/IJNS.180304 https://www.americaspg.com/articleinfo/21/show/1056