Andrii Zvarun was director of the Smoloskyp publishing house during 1972-1992 and member of the Smoloskyp quarterly editorial board in 1978-1989. An activist of Ukrainian human rights movement in the US, he led the Washington Helsinki Guarantees for Ukraine Committee in 1976-1982, which was formed at the initiative of the Information Service of Smoloskyp. After World War II, Zvarun with his family moved from Soviet Ukraine to Germany and later to the US, where he got his degree in microbiology from Ohio University. In 1972, he joined Smoloskyp's human rights activities. He organized a series of protest campaigns against political repression in Soviet Ukraine, prepared Smoloskyp press releases, participated in international human rights conferences, including the first International Sakharov Hearing in Copenhagen. In 1977, he spoke on Ukrainian dissident movement and the Ukrainian Helsinki Human Rights Group at the US Congress. Zvarun managed to receive the majority of documents of the Ukrainian Helsinki Human Rights Group from the Group’s founder, Mykola Rudenko. The documents were later published by Smoloskyp.

Zvarun also took an active role in the campaign for liberating Nina Strokata, a repressed Ukrainian microbiologist and a founding member of the Ukrainian Helsinki Group. As a result of the campaign, Strokata was accepted for membership in the American Society for Microbiology that later helped her and her husband, Sviatoslav Karavanskyi, to emigrate to the US.