* King's health is improving, TV says
* Crown prince, also in his 80s, governing kingdom
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RIYADH, Nov 24 (Reuters) - The health of Saudi Arabia's ageing King Abdullah, who is in New York for medical treatment on his back, has shown noticeable improvement, Al Arabiya television said on Wednesday.
The Saudi-owned television gave no further details.
The king, thought to be around 86 or 87, arrived in New York on Monday. He was seeking treatment after a blood clot complicated a slipped spinal disc, the state news agency SPA said earlier.
A frail Crown Prince Sultan has returned from abroad to govern the world's largest oil exporter, which is keen to show its allies in Washington and elsewhere there would be no power vacuum as health problems beset its octogenarian rulers.
With both Abdullah and Sultan in their 80s, the next in line would be conservative Interior Minister Prince Nayef, at a relatively youthful 76. Nayef would still need the approval of Saudi Arabia's "Allegiance Council" to become king.
Diplomats say Sultan, who is also defence minister and has major health problems of his own, has been much less active during his convalescence in Morocco. (Editing by Myra MacDonald)
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