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As we talk, Adm Fallon cautions against setting arbitrary deadlines on withdrawing troops from Iraq. When I suggest that is exactly what Barack Obama's campaign has been doing, he repeats his advice against setting calendar dates and suggests the next president should set overall policy but, after that, "let's let those that are best equipped to work the details of this... there are lots of people in the food chain who can deal with this pretty effectively".

This sounds like a clear tilt at Mr Obama who has insisted recently that he will be making the decisions on this matter. Never mind that President Bush and the Iraqi government have also had to become increasingly explicit about how long US combat troops will stay in Iraq, as they negotiate a treaty on their future strategic relationship, the admiral's real point is that timing should be left to the experts.

All of this makes me wonder how difficult Mr Obama's future relations with the military might be. He is no ignoramus on military matters or ¾±²Ô²µÃ©²Ô³Ü±ð in talking to military officers, having done his time on the Senate Armed Services Committee. But he does not have the natural empathy with them that a decorated fighter pilot and former prisoner of war like John McCain does.

If President Obama were to set himself on a collision course with military chiefs - be that on budgets or getting out of Iraq - that would undoubtedly cause him potent political difficulties. The terms of these military debates formerly so dry, and policy-wonk dominated have become very emotive since 9/11. Many millions of Americans still consider the nation is at war, and that the blood of thousands lost in Iraq or Afghanistan should not have been shed in vain.

Given the enormous strains of the past years - caused in part by the Administration's epic mis-management of the invasion of Iraq (and early years of occupation) - it is actually remarkable how limited the strains have been with President George Bush. True, one or two major generals gave damming testimony in Congress. True also that many military families share the wider public's opposition to long term operations in Iraq or Afghanistan. But for the most part President Bush has maintained a cosy relationship with his top brass.

General Jack Keane, former head of the US Army, and a key advocate of the Iraq surge strategy, once told me that things had gone wrong in Iraq because the president had been "too deferential" to his generals. That seems hard to credit, given the way America was driven into the Iraq war by ignorant "policy types", but Gen Keane's remarks make sense when one considers that having got into Iraq, the president gave his commanders a pretty free hand about how to get out, even when, in 2005-6, it started to become obvious that America's rushing for the door was making things in that country markedly worse rather than better.

While the standard liberal critique of General David Petraeus, the commander in Iraq who has been nominated as Adm Fallon's successor at CentCom, is that he is too close to the White House, and has been too ready to implement their surge policy, this has never seemed very convincing to me. Based on my own observations of Gen Petraeus and those around him, I think it was more a case of the general believing that avoiding defeat in Iraq was an imperative mission, which he, the professional military, and the president could make their common cause. Like so many of his generation, Gen Petraeus was determined to avoid "another Vietnam", and the president, having pinned his political legacy on Iraq was willing to give the general the resources to succeed.

Thinking back to times before 9/11, I can certainly remember that relations between President Bill Clinton and his military chiefs, often seemed pretty poisonous. One regularly heard them disparage him as ignorant of military affairs and bereft of any big ideas. President Clinton gave the US military directives - for example designed to avoid casualties during Nato's 1999 Kosovo campaign - that they considered idiotic, and some of them certainly let us know about it.

So Adm Fallon's views appear to constitute a warning against the doctrinaire approach - be that the neo-con one on Iran or the Obama campaign's presumption that withdrawal from Iraq can be driven entirely by political imperatives. Perhaps it is a plea also for whoever is elected president to take senior military advice seriously, unless they want to risk a turbulent relationship with their top brass.

Watch Mark Urban's interview with Admiral Fallon on Newsnight, Friday 8 August on ³ÉÈË¿ìÊÖ TWO.