The European pillar inside NATO.
NATO resources, in particular air resources, are needed for the EU's Rapid Reaction Force to be effective, but this requires the co-operation of America, Canada, Turkey and other non-EU NATO members.
The future
The EU Constitution propose stronger EU control of Eurogroup resources. According to the Finnish head of the EU military staff, Gustav Hägglund, the EU military will merge with NATO in due time.Links
http://www.nato.int/