This thesis is an extension of the work done by Karzel, Kosiorek and Matras (Point symmetric 2-structures). Let S be a non empty set , P := S × S the product set and let G1= { S × {x} | x ?? P} and G 2 = {{x} × S | x ?? P} be the sets of generators . Then (P, G1,G 2 ) is a net i.e . forall p ?? P, forall i ?? {1,2} ? X ?? G i such that p ?? X and if X ?? G1, Y ?? G 2 then |X ? Y| = 1. A subset is called a chain if forall X ?? |C ? X| = 1. Let C e the set of all chains of the net (P, G1,G 2 ), for a,b ?? P let a ? b := ab = [a] 1 ? [b] 2 . Let P (2) := { (a,b) ?? P 2 |a ? b a,b} and if A,B,C ?? C Let : P ? P; x [B?[x] 2 ] 1 ? [A ?[x] 1 ] 2 and . Then is an involutory antiautomorphism mapping each chain onto a chain. Two distinct chains A , B are called orthogonal, denoted by A ? if (B) = B and if K C then ( P; G1 ; G2 ; K) is called chain structure. A chain structure i called symmetric chain structure if forall K ?? K : (K ) = K. A chain structure ( P; G1 ; G2 ; K) is called 2-structure if forall (a,b) ?? P (2) : ? 1 K ?? K: a,b ?? K- we set K = .