The medium-height, slightly built Giallelis was twenty-one years old in mid-1962, upon Elia Kazan's arrival in Greece looking for someone who could capture his uncle's life in 1890s Anatolia and the struggle to achieve his determined dream of immigrating to the United States.
In his autobiography, Elia Kazan: A Life, the director describes the details of his search for "a ferret, not a lion", someone who, like his uncle, did not always behave honorably, but had "my boy's single redeeming quality, devotion to his father and family".
The only son in a family with four daughters, he nevertheless impressed Kazan with his sincerity and deeply felt reminiscences of his Communist father's death in the aftermath of the Communist–centrist/rightist struggle in the Greek Civil War.
The New York Times' Bosley Crowther, in his December 16, 1963 review of the film, noted that "Greek lad Stathis Giallelis (pronounced STAH-this-Ya-lah-LEASE) is incredibly good as the determined hero, putting fire and spirit into the role".
In the months between the end of production and its December release, he completed a cameo role in Nikos Koundouros' 1963 Greek art film Mikres Afrodites (Young Aphrodites).
Ultimately, however, in the 16-year period between 1964 and 1980, he appeared in front of the camera only seven more times in widely spaced film projects, only three of which (Cast a Giant Shadow, Blue and The Children of Sanchez) were American productions.
The all-star epic about a Jewish-American army officer's key leadership role in winning the battles which led to the 1948 establishment of Israel, found him fifth-billed after Kirk Douglas (as the central figure, Colonel Mickey Marcus), Senta Berger, Angie Dickinson and James Donald.
The World War II heroics on display gave top billing to American Ty Hardin who, in the late 1960s and early 1970s, appeared in a number of European-made action films and Spaghetti Westerns.
In 1974, Jules Dassin and his wife Melina Mercouri used the donated services of many top entertainment personalities to produce The Rehearsal, an angry docudrama which reconstructed the events leading to the killing of some forty students in Athens, as they protested against the heavy-handed rule of the Greek Junta.
As a Greek living abroad, Giallelis was invited to participate along with Olympia Dukakis, Mikis Theodorakis and other celebrities of varying nationalities, such as Laurence Olivier and Maximilian Schell.
Now able to return to his homeland, Giallelis appeared in esteemed Greek director Pantelis Voulgaris' Nineteen Eighty-Four-like allegory Happy Day, playing one of the leads in the story about imprisonment and repression in an unspecified European-style society.
Hall Bartlett's adaptation of the Oscar Lewis novel was filmed on location in Mexico and starred native-born Anthony Quinn as his country's putative everyman, Jesus Sanchez.
Giallelis received yet another fifth billing, following two veteran Mexican actresses, Dolores del Río and Katy Jurado, as well as Venezuelan Lupita Ferrer who, at the time, was married to Hall Bartlett.