RELATIONS between Islam Karimov, president of Uzbekistan, and his counterpart in Kazakhstan, Nursultan Nazarbayev, have long been soured by their tussle for regional primacy in Central Asia. But the two ageing autocrats can be pragmatic. So on March 27th Mr Karimov granted an audience to Mr Nazarbayev’s foreign minister, Erlan Idrissov, in his residence in the capital Tashkent. The two ageing leaders seem to want to give each other a helping hand.

Television footage of the meeting was closely studied. It was the first public glimpse of the 75-year-old Mr Karimov since he was rumoured to have suffered a heart attack on March 19th. His daughter, Gulnara, had taken to Twitter to deny that his health was precarious. But it took his reappearance to quell the speculation.

The source for the health scare was a former rival and exiled opposition leader, Muhammad Salih. But the rumour hit a raw nerve in Uzbekistan and elsewhere. Many worry that the withdrawal of Western troops from Afghanistan could destabilise Central Asia, including Uzbekistan, which serves as a transit point for NATO. A disorderly transition in the region’s most populous country, with 30m people, would not help.

Mr Karimov has been in office since the last days of the Soviet Union and shows few signs of wanting to release his iron grip on power. But his age and now questionable health make the succession critical. Several possible contenders exist among the regime’s apparatchiks, such as Rustam Inoyatov, the security chief, who is often described as the country’s second most powerful man. A more urbane candidate is Rustam Azimov, the first deputy prime minister. The hardline prime minister of ten years, Shavkat Mirziyoyev, is also a possibility.

Then there is Gulnara herself. “Googoosha” (her father’s pet name for her) is a 40-year-old pop diva, fashion designer, charity impresario, entrepreneur and diplomat. She cuts a colourful swathe through Tashkent’s grey corridors of power, but the hard-faced men who reside there will surely resist such a seemingly flighty president. In the uncertain post-Karimov era, the job will demand political nous and clout. She also happens to be widely loathed in the country.

Kazakhstan faces similar problems. Mr Nazarbayev, now 72, has also been at the helm since the Soviet era. Assumed to have been treated for prostate cancer, the succession is even discussed relatively openly by analysts.

Changes in leadership in Central Asia are about not just the usual struggle for political power, but the elite’s fierce fight to protect its economic interests. In oil-rich Kazakhstan, the region’s magnet for foreign investment, both the wealthy and the middle class worry about losing what they have built for themselves. The rich have squirrelled money abroad.

Disaffection with the authorities is spreading in a population dismayed by rising food prices, endemic corruption, and health-care and education systems that are still lousy despite increased government spending. The killing in December 2011 of at least 15 protesters in Zhanaozen, an oil town in the west of Kazakhstan, also still rankles.

Tolganai Umbetaliyeva, co-author of a recent book mapping out different routes for a transition from Mr Nazarbayev, calls the situation “tense and alarming”. Ideal but unlikely, she says, would be a change in the political system. Dynastic transitions do not always go smoothly. Like Mr Karimov, Mr Nazarbayev has a daughter discussed as a potential successor.

Ms Umbetaliyeva thinks that, despite the elite’s resistance to more democracy, the people want a say in the choice of successor. It is more likely, however, as in Uzbekistan, that a weak compromise candidate whom all factions can agree on, for a time, will be installed behind the scenes by the power-brokers. Either that, or a new strongman will emerge.