IN 1989, the ruling Politburo of the Soviet Union chose new leaders for two of the empire's Central Asian republics. Twenty-six years later, Nursultan Nazarbayev of Kazakhstan and Islam Karimov of Uzbekistan are still in power. They have weathered the Soviet Union's collapse, wars in Afghanistan and other neighboring nations, the rise of China and the spread of Islamist terrorism with a mix of repression, crony capitalism, corruption and the cultivation of competing powers, including the United States. Now, like leaders across Eurasia, they are wondering if they can survive the revived imperialism of Russia under Vladimir Putin.