en عمومى General پژوهشي Research paper Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concepts of graded semi J_gr-2-absorbing and graded weakly semi J_gr-2-absorbing submodules of M and study the behavior of these notions under several constructions. A proper graded submodule N of M is said to be a graded semi J_gr-2-absorbing (resp. graded weakly semi J_gr-2-absorbing) submodule of M if whenever r_g &isin; h(R) and m_h &isin; h(M) with r_g²m_h&isin; N (resp. 0&nbsp;&ne; r_g²m_h &isin; N), then either r_gm_h &isin; N + J_gr(M) or r_g²&isin; (N + J_gr(M) :_R M), where J_gr(M) is the graded Jacobson radical.<br> &nbsp; Graded semi $J_{gr}$-2-absorbing submodules, Graded weakly semi $J_{gr}$-2-absorbing submodules, Graded $J_{gr}$-2-absorbing submodules. 101 110 http://ijmsi.ir/browse.php?a_code=A-10-2797-3&slc_lang=en&sid=1 Shatha Alghueiri ghweiri64@gmail.com 100319475328460011255 100319475328460011255 No Department of Mathematics and Statistics Jordan University of Science and Technology P.O.Box 3030, Irbid 22110, Jordan Khaldoun Al-Zoubi kfzoubi@just.edu.jo 100319475328460011256 100319475328460011256 Yes Department of Mathematics and Statistics Jordan University of Science and Technology P.O.Box 3030, Irbid 22110, Jordan