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 along with some model extensions designed to extend its flexibility and applicability. The model develops flow management strategies involving combinations of ground and airborne holding. The paper illustrates the complex nature of EU ATFM 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 EU ATFM context as a result of the interactions among traffic flows.