With physical problems such as these - he also has a muscle degeneration condition - most men might be expected to slow down a little. Mr Eagleburger is not that type of person, which is a good thing, given his appointment this week as Acting US Secretary of State in place of James Baker, who departs to take control of George Bush's election campaign.
There is much that is unusual about Mr Eagleburger, not least that he named each of his three sons Lawrence, partly, he concedes, out of ego and partly to bamboozle the Social Security Department. But he is also the first career diplomat, with more than 30 years in the service, to reach the top spot at the State Department or even to become Deputy Secretary of State, as he has been since 1989 under Mr Baker.
This depth of experience and his almost unique familiarity with the diplomatic community around the world has much to do with the respect in which he is generally held. It helps also that he is a very funny and very frank man. Asked on Thursday at the time of his appointment why, on top of everything else, his arm was in a sling, he replied: 'You should have seen the other guy.' It was in fact prescribed after a biopsy related to the muscle disease.
As Deputy Secretary, Mr Eagleburger has tended to look after those areas of policy that Mr Baker did not care to handle, such as Haiti and Eastern Europe. He went on two secret missions to China with the National Security Adviser, Brent Scowcroft, after Tiananmen Square, and was also dispatched during the Gulf war to Israel to dissuade them from attempting any retaliation against Iraqi Scud attacks.
However, there are details about periods in that career that have opened Mr Eagleburger, and his elevation this week, to some criticism. Notable among them are his past associations with former Yugoslavia, where he was US ambassador, 1977-1980, and his close ties to Henry Kissinger, for whom he worked both in the Nixon and the Ford administrations. And between 1984 and 1988, he took a break from the State Department to work with his former mentor's Washington consultancy firm, Kissinger Associates.
While at the firm, Mr Eagleburger profited from his past diplomatic links in personal business connections with Yugoslavia, taking a board position on a US- based Yugoslav bank, LBS Bank, and acting as chairman of Yugo- America Inc, importing cars.
These interests and his past contacts with the old, Serb-dominated, regime in Belgrade have opened him to accusations from Congress that he has been partly responsible for the slow recognition by the administration of the depth of the Balkan crisis.
The very fact of his career-diplomat background has also raised concerns that he does not have the political base and influence expected of a Secretary of State. Mr Baker, whose intensely political background is evidenced by his transfer to the Bush-Quayle campaign, ran US foreign policy with a tight circle of policy advisers. One layer down, Mr Eagleburger was left actually to run the State Department apparatus with little access to high policy-making. Nor is he thought to be inside the minds of either Mr Baker or Mr Bush, although he has perfectly workable relationships with both of them.
'Larry doesn't have the political clout, but I think he has a solid grasp of policy issues,' said Helmut Sonnenfeldt, also a past aide to Mr Kissinger. He added that when Mr Baker was away, Mr Eagleburger 'was very often relied on to conduct policy because of Baker's preoccupations'.
Mr Eagleburger, who has said he intends retiring next January, is bound also to be seen by partners worldwide as only a caretaker and even a lame duck.
He does, however, have one highly conductive wire into the White House - to Mr Scowcroft, his buddy from Kissinger days and who himself has strong Yugoslav credentials. The two men consult each other regularly and have been known to infuriate other White House staffers by talking to each other in Serbo- Croat at meetings, a language both men speak fluently.
Inevitably, the Democrats have decried the loss of Mr Baker from the State Department at a time of such high international stakes: in the Balkans; the Middle East; and the Gulf. But the criticism has not extended to the choice of Mr Eagleburger as the caretaker replacement. Jo Biden, the leading Democrat Representative, remarked of him: 'I've always been impressed. He is Kissinger without his warts. Kissinger with a clear moral compass.'
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