  Gomory and Hu proved that if $ G $ is a finite graph with non-negative
weights on its edges, then there exists a tree $ T $ (called now Gomory-Hu
tree) on $ V(G) $ such that for all $ u\neq v\in V(G) $ there is an $ e\in E(T)
$ such that the two components of $ T-e $ determines an optimal (minimal
valued) cut between $ u $ an $ v $ in $ G
  $. In this paper we extend their result to infinite weighted graphs with
finite total weight. Furthermore, we show by an example that one can not omit
the condition of finiteness of the total weight.
