Much of the reason why the EU haven't got a security policy and regime on their own has to do with disagreements within the EU member states.  The US has actually spoken positively of a stronger defense presences by the EU.  The disagreement is over how NATO are to fit into that equation and the insistence of US control over certain aspects within the Defense organization, some of it quite reasonable since the US are by fare the greatest contributer, of all the member states, to the organization both money wise and equipment wise.  

If the EU countries can resolve their differences then I am quite sure that the ESDP will develop much quicker and NATO will function more like a defense and security forum with the infrastructure ready to function as a military defense organization if need be.  This will guarantee a close relationship to the US and at the same time give EU its own military capability.  The NATO structure will evolve from essentially a one pillar system, the US, into a two pillar system consisting of Europe and the US as equal partners.  

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