In this paper, we consider the finitely presented groups Gm and K(s, l) as follows; Gm = 〈a, b|a = b = 1, [a, b] = [a, b], [a, b] = [a, b]〉 K(s, l) = 〈a, b|ab = ba, ba = ab〉; and find the n-commutativity degree for each of them. Also we study the concept of n-abelianity on these groups, where m,n, s and l are positive integers, m,n ≥ 2 and g.c.d(s, l) = 1.