Let D be a directed Eulerian multigraph, v be a vertex of D. We call the common value of id (v) and od(v) the degree of v, and simply denote it by dc. Xia introduced the concept of the T-transformation for directed Ealer tours and proved that any directed Euler tour (T)-transformation graph Eu(D) is connected. Zhang and Guo proved that Eu(D) is edge-Hamiltonian, i.e., any edge of Eu(D) is contained in a Hamilton cyclc of Eu(D). In this paper, we obtain a lower bound ∑Γ∈Q(dv-1)(dv- 2)/2 for the connectivity of Eu(D), where Q={v∈V(D)|du≥2}. Examples are given to show that this lower hound is in some sense best possible.