Air traffic flow management in Europe has to deal with capacity constraints in en route airspace, in addition to the usual capacity constraints at airports. The en route sector capacity constraints, in turn, generate complex interactions among traffic flows. A new deterministic mathematical model for the European ATFM problem is presented. The model designs flow management strategies involving combinations of ground and airborne holding. The paper illustrates the complex nature of solutions, the benefits that can be obtained by assigning some airborne holding delays in addition to ground delays, and the issues of equity that arise in the context as a result of the interactions among traffic flows.