Studying the commutativity of Г-near ring M by investigate some results concerning of Г-derivation and generalized Γ-derivation of M and studying special kind of Γ-derivation called the strong commutativity preserving Γ-derivation (SCP) on M and on an invariant subset of M when M is a prime and semi prime ring. Also studying acts freely of some mapping as centralizer reveres centralizer generalize Γ-derivation and Γ-derivation of M.