NEUTROSOPHIC DUPLET STRUCTURES   Abstract. The Neutrosophic Duplets and the Neutrosophic Duplet Algebraic Structures were introduced by Florentin Smarandache [1, 2, 3] in 2016.   Let U be a universe of discourse, and a set D included in U, endowed with a well-defined law #. 1. Definiton of the Neutrosophic Duplet (ND). We say that , where a, and its neutral neut(a) belong to D, is a neutrosophic duplet if: 1) neut(a) is different from the unitary element of D with respect to the law # (if any); 2) a#neut(a) = neut(a)#a = a; 3) there is no opposite anti(a) belonging to D for which a#anti(a) = anti(a)#a = neut(a). 2. Example of Neutrosophic Duplets. In (Z8, #), the set of integers with respect to the regular multiplication modulo 8, one has the following neutrosophic duplets: <2, 5 >, <4, 3>, <4, 5>, <4, 7>, and <6, 5>.  Proof: Let Z8 = {0, 1, 2, 3, 4, 5, 6, 7}, having the unitary element 1 with respect to the multiplication # modulo 8. 2 # 5 = 5 # 2 = 10 = 2 (mod 8), so neut(2) = 5 ≠ 1. There is no anti(2) ∈ Z₈, because: 2 # anti(2) = 5 (mod 8), or 2y = 5 (mod 8) by denoting anti(2) = y, is equivalent to: 2y - 5 = M8 {multiple of 8}, or 2y - 5 = 8k, where k is an integer, or 2(y - 4k) = 5, where both y and k are integers, or: even number = odd number, which is impossible. Therefore, we proved that <2, 5> is a neutrosophic duplet. Similarly for <4, 5>, <4, 3>, <4, 7>, and <6, 5>. A counter-example: <0, 0> is not a neutrosophic duplet, because it is a neutrosophic triplet: <0, 0, 0>, where there exists an anti(0) = 0.   3. Definiton of the Neutrosophic Extended Duplet (NED). Let U be a universe of discourse, and a set D included in U, endowed with a well-defined law #. We say that , where a, and its extended neutral eneut(a) belong to D, such that: 1) eneut(a) may be equal or different from the unitary element of D with respect to the law # (if any); 2) a#eneut(a) = eneut(a)#a = a; 3) there is no extended opposite eanti(a) belonging to D for which a#eanti(a) = eanti(a)#a = eneut(a).   4. Definition of Neutrosophic Duplet Strong Set (NDSS). A neutrosophic Duplet Strong Set is a set D, such that for any x ∈D there is a neut(x) ∈ D and no anti(x) ∈ D.   5. Definition of Neutrosophic Duplet Weak Set (NDWS). A neutrosophic Duplet Weak Set is a set D, such that for any x ∈D there is a neutrosophic duplet included in D, such that x = y or x = neut(y).   6. Definition of Neutrosophic Extended Duplet Strong Set (NEDSS). A Neutrosophic Extended Duplet Strong Set is a set D, such that for any x ∈D there is an eneut(x) ∈ D and no eanti(x) ∈ D.   7. Definition of Neutrosophic Extended Duplet Weak Set (NEDWS). A Neutrosophic Extended Duplet Weak Set is a set D, such that for any x ∈D there is a neutrosophic duplet included in D, such that x = y or x = eneut(y). 8. Definition of Neutrosophic Duplet Strong Structures (NDSStr). Neutrosophic Duplet Strong Structures are structures defined on the neutrosophic duplet strong sets.   9. Definition of Neutrosophic Duplet Weak Structures (NDWStr). Neutrosophic Duplet Weak Structures are structures defined on the neutrosophic duplet weak sets.   10. Definition of Neutrosophic Extended Duplet Strong Structures (NEDSStr). Neutrosophic Extended Duplet Strong Structures are structures defined on the neutrosophic extended duplet strong sets.   11. Definition of Neutrosophic Extended Duplet Weak Structures (NEDWStr). Neutrosophic Extended Duplet Weak Structures are structures defined on the neutrosophic extended duplet weak sets.   References [1] F. Smarandache, Neutrosophic Theory and Applications, Le Quy Don Technical University, Faculty of Information technology, Hanoi, Vietnam, 17th May 2016. [2] Florentin Smarandache, Neutrosophic Duplet Structures, Joint Fall 2017 Meeting of the Texas Section of the APS, Texas Section of the AAPT, and Zone 13 of the Society of Physics Students,  The University of Texas at Dallas, Richardson, TX, USA, October 20-21, 2017,  Hybrid Operators, Modal Logic, Hedge Algebras. And Applications. Pons Editions, Bruxelles, 323 p., 2017; CHAPTER IX: 127-134 Neutrosophic Duplets 127 Definition of Neutrosophic Duplet. 127 Example of Neutrosophic Duplets. 127 Neutrosophic Duplet Set and Neutrosophic Duplet Structures 130 Definition of Neutrosophic Duplet Strong Set 130 Definition of Neutrosophic Duplet Weak Set 130 Proposition. 131 Theorem 131 Example of Neutrosophic Duplet Strong Set 132-133