In this paper

we obtain upper bounds of the diameters for both undirected and directed Euler tour transformation graphs.(l) Let G be an undirected Eulerian multigraph and Q(G) = {v∈ V(G) |d(v) ≥ 4}. Let λ(G)= and diam (E.(G)) denote the diameter of the Euler tour (K-) transformation graph E.(G) of G.Then we have diam (E.(C)) ≤λ(G) - 3.(2 ) Let D be a directed Eulerian multigraph

d (v) = id(v) - 0d (v) and-Q(D) ={v∈V (D) | d (v) ≥2 }.Let and diam (E.(D)) denote the diameter of the directed Euler tour (T-) transformationgraph E.(D) of D. Then we haveExamples are given for showing that the two upper bounds are in some sense best possible.