While conducting his research into the painted caves, Eshleman continued his work as a translator. Working with José Rubia Barcia, he completes new translations of César Vallejo's Complete Posthumous Poetry. Published by the University of California Press in 1978, the collection won the National Book Award for Translation the following year. Working with Norman Glass, Eshleman translated several major works by Antonin Artaud, published as Four Texts in 1982, and, beginning in 1977, working with Annette Smith, he translated the complete poetry of Aimé Césaire in several volumes. This work is supported by a translation grant from the National Endowment for the Humanities and, in 1981, it wins the Witter Bynner award from the Poetry Society of America.