Later Zvyahilsky defended his doctorate on the subject "Geomechanical foundations of landslides of the earth surface above mines, which can be eliminated" (Institute of geotechnical mechanics of the National Academy of Sciences of Ukraine).

In March 1990, as a member of the Communist Party of the Soviet Union, Zvyahilsky was elected to the Parliament of Ukraine from the 112th electoral district.

In 1994, Zviahilskyi, being perceived as affiliated with Leonid Kravchuk, was accused of having stolen some $20 million by Ukrainian President Kuchma during his term as acting Prime Minister, and he fled to Israel in fear for his life.

Zvyahilsky became a member of the Verkhovna Rada (parliament), representing the ruling Party of Regions, and owner of the Zasyadko coal mine in Donetsk.

[8] In the 2014 parliamentary election, Zvyahilsky was re-elected into parliament again as an independent candidate in single-member districts number 45 situated in the Kyiv Raion of Donetsk; this time with 72.73% of the votes.

[9] In his constituency, only a handful of polling stations were open due to the war in Donbas; this led to Zvyahilsky winning a seat with only 1,450 votes.