Abstract: Let R be an associative ring. The major proposal of the present study is to introduce the concept of relatively commuting of R. Let S be a nonempty sub set of R, A mapping δ:S→R is called relatively commuting mapping on S if [δ(s), s]n = 0 for all ∈S and a fixed positive integer n≥2. We describe the relationship between the new concept and the concept of commuting mapping. Moreover, we looking for some necessary conditions under which these two concepts equivalence.