THE tremors from the political earthquake which struck Russia last month are now shaking the structures of Communist power in distant Soviet Central Asia.For three days, a coalition of Islamic and democratic movements has massed thousands of protesters in the central square of Dushanbe, the capital of the republic of Tadzhikistan, calling for reversal of what they call a Communist-led "reactionary coup." The uprising is the most visible sign that the anticommunist democratic revolution that followed last month's failed coup is triggering protests against the conservative Communist regimes still in power in most of the Muslim republics of Central Asia. Neighboring Uzbekistan has seen sporadic protests by similar alliances of Islamic and democratic organizations during the past month. The Communist organizations in Central Asia have tried to maintain power while accommodating, at least superficially, the changes sweeping the Soviet Union. Leaders such as Uzbek President Islam Karimov openly supported the attempted coup, but after its failure, they quickly joined the parade of republics declaring independence. The party organizations in Uzbekistan, Turkmenia, and Tadzhikistan all formally dissolved, then simply adopted titles such as the Socialist Party of Tadzhikistan, or the People's Democratic Party of Uzbekistan. Only in Kirgizia, where the democrats took power last fall, did real opposition to the coup emerge. Neighboring Kazakhstan, led by President Nursultan Nazarbayev, also has long been in the forefront of reforms, particularly in moves toward a market economy. But the events in Tadzhikistan, under former hard-line Communist leader Kakhar Makhkamov, suggest that the Communists may not be able to hold onto power easily in the traditionally more conservative Muslim republics. Following the coup's failure, Mr. Makhkamov was forced to resign after a vote of no-confidence in the parliament on Aug. 31. His open support of the coup had made him unpalatable, particularly in Moscow, where he was clearly out of step with the new leadership. He was replaced by Kadreddin Aslonov, a more moderate party official, pending a new election scheduled for Oct. 27. Mr. Aslonov appears to have surprised the party bosses when on Sunday he banned the renamed party and ordered its assets seized. The mayor of Dushanbe then backed protesters pulling down the massive statue of Vladimir Lenin in the central Freedom Square. The Communist-controlled parliament retaliated on Monday, by annulling these actions, declaring a state of emergency, and installing former Communist Party boss Rakhman Nabiyev as acting president. These moves provoked demonstrations organized by a coalition of the Democratic Party of Tadzhikistan, the Rastokhez popular movement, and the Islamic Renaissance Party. The alliance, in a statement issued on Sept. 24, called for the removal of the state of emergency, the dissolution of the "Communist parliament," and holding democratic elections with foreign observers. Their goal, the coalition said, is "not an Islamic state, as the Communists have been claiming, but a law-governed democratic state of civil peace." The Moscow authorities have not responded directly to the events in Dushanbe with the important exception of an announcement on Monday that the small Soviet Army contingent based in the republic had been ordered not to enforce the state of emergency. "I think the opposition has a chance," comments Tair Tairov, a Moscow-based expert on Central Asia recently returned from his native Uzbekistan. He foresees a "long period of confrontation," but adds, "The process has started there. You cannot return to Communism there." If the Communists should fall, it is far from clear who will inherit the mantle of power, however. The democratic movement in the Central Asian republics is weak, led by Westernized intellectuals without a large popular base. The Islamic movements, particularly in Uzbekistan, Turkmenia, and Tadzhikistan, are far more popular and growing in political strength.