Directors of state firms and local council leaders won most of the 27 seats.
Just three were won by candidates who were registered communists.
Kuchma, inaugurated less than a month ago, has clashed with the conservative assembly over his pledge to reform the economy.
"The communists will no longer be the leaders in parliament, because the unaffiliated majority is taking a pragmatic, centrist stance," said Oleh Soskin, a political analyst who is based in Kiev. #
"These by-elections indicate Ukrainian society is casting off the communist ideology. Ukrainians voted for people who can do something -- managers, heads of large enterprises -- those who make a difference in the economy," he continued.
The by-elections, held in constituencies where voter turnout was less than 50 percent in March general elections, brought the number of elected deputies to 393 out of 450 seats available.
Another series of votes is scheduled for November.
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