Some of the East-Central European countries that had had Marxist-Leninist regimes were slower than others, in voting those regimes out of power.
In Poland, even though the 1989 election had been rigged to produce a Communist victory, the Solidarity union-cum-party was able to elect a prime minister from its own ranks.
East Germany, Czechoslovakia and Hungary followed in short order, early in 1990.
In Czechoslovakia, Vaclav Havel, a dissident playwright who had been a political prisoner, was elected president on December 29, 1989. The country then voted in a free parliamentary election on June 8, 1990. The Civic Forum, a broad anti-Communist coalition, won a majority.
Then, in May 1990, Hungary elected a parliament, resulting in a coalition government headed by the center-right MDF party.
Poland eventually threw off the last vestiges of its Marxist-Leninist past. Lech Walesa, the Solidarity leader, was elected president in December 1990. A fully free parliamentary election followed on October 27, 1991, putting a center-right coalition into office. However, in Poland, as in many of these countries, center-left parties with roots in the Communist past, have held power at various subsequent times, but they haven't significantly strayed from the democratic market-oriented path that was set in 1989.
As I noted here, Romania's dictator Nicolae Ceausescu did not go gently into that good night, as some of his counterparts did. He had to be shot out of office. After that, the National Salvation Front (FSN), which largely consisted of lower-level Communist functionaries from the Ceausescu regime, held on to power for years. It took until 1996 for an opposition party to be elected. But Romania has progressed at its own pace, and is now a member of NATO and the EU.
On June 10, 1990, Bulgaria held a multi-party election in which the Socialists (a reformed version of the Communist Party) won a majority. Another election, on October 13, 1991, produced a coalition government led by the anti-Communist Union of Democratic Forces. Sources on the Web describe the 1991 election as Bulgaria's first fully democratic one. But I could not find any description of the ways in which the 1990 election fell short. Any comments on that would be appreciated.
Albania was odd man out, among the European Marxist-Leninist countries. It was the only one that maintained closer ties to China than to the Soviet Union, after the rift opened up between Moscow and Beijing, circa 1960. Albania maintained a Stalinist approach to government, which alienated it from Stalin's successors in Moscow and, later, to Mao Zedong's successors in Beijing. Those policies left it as perhaps the worst economic basket-case on its continent. In 1992, the Communists were voted out of power in Albania.