This paper is devoted to multiflow in Eulerian network. It contributes to describing the set \(R\) of feasible vectors. First, the feasible vectors are shown to be bases of a polymatroid \((T,p)\) forming a proper part of the polytope defined by the supply-demand conditions. \(p(V)= \max\{\xi(V):\xi\in R\}\), \(V\subseteq T\) is described by a max-min theorem. Second, the lexicographically minimum (and thereby maximum) feasible vector is found, for an arbitrary ordering of \(T\).