[14] In the 1960s Tarnawsky switched fully to writing in English, first in fiction and then in poetry; although in the latter he subsequently made Ukrainian versions of the English-language works (the volume This Is How I Get Well (1978) and the next five collections).

He joined the group of innovative American writers Fiction Collective (later FC2) and published with it the novels Meningitis and Three Blondes and Death, both of which received high praise from US critics.

(Three Blondes and Death, for instance, was compared by one reviewer to the skyscrapers of Mies van der Rohe and Gropius which towers over the cottages of contemporary American fiction.)

His works now show elements characteristic of postmodernism, such as polystylism, collage, pastiche, and the taking on of many, sometimes opposing, stances or masks (for instance, the poetry collection An Ideal Woman (1999), the book-length poem U ra na (1992) and The City of Sticks and Pits (1999), as well as the cycle of plays 6x0 (1998), all in Ukrainian).

His own Ukrainian-language version of the English-language collection of stories Short Tails that shows the influence of existentialism, absurdism, and postmodernism, was published in Ukraine in 2006.

The Placebo Effect Trilogy, three collections of interrelated mininovels—Like Blood in Water (revised edition), The Future of Giraffes, and View of Delft—were published in 2013.

The trilogy and its volumes may be viewed as a novel/novels, unified not by characters and events, as is the case in traditional fiction, but by the common topics of existential despair, fear of death, and alienation, which, like motifs in music, bind them into a whole.

His two 2019 novels have uncharacteristically realistic settings—Warm Arctic Nights is a fictionalized memoir of his early years in Poland and Ukraine, presented in the form of an interview, and The Iguanas of Heat with its detailed US and Mexico settings and ostensibly a suspense story, is a painstaking deconstruction of a sterile marriage.

Claim to Oblivion, his book of selected essays and interviews in English, which deal primarily with his own literary works and the issues he tackles in them, was published in 2016.

In 1997, the first four plays from 6x0—The Boring Bitch of Despair, Female Anatomy, Not Medea, and Dwarfs—received a public reading by actors of the drama studio of National University of the Kyiv-Mohyla Academy in Kyiv.

Tarnawsky is also the author of the libretto of the opera Not Medea, based on his eponymous play, by the Ukrainian-American composer Virko Baley, part of which was staged in New York City in 2012.

Tarnawsky has been married three times: Of Polish origin, Zalewska received an MA degree in Ukrainian philology from the Krakow Jagiellonian University in 1999 and met her future husband in Kyiv in 1998, when she was on an exchange student program.