Both multiple objectives and multiple hierarchies minimum cost flow problems with fuzzy costs and fuzzy capacities in the arcs are investigated. To reduce the complexity, a possibility programming is used to handle the vagueness in the parameters. Fuzzy approach can considerably simplify the problem and thus a fairly general multi-level problem can be solved reasonably easily in spite of the fact that the multi-level problem is NP-hard and very difficult to solve. Several numerical examples are considered to illustrate the approach.