Dzhigarkhanyan's portrayal of Socrates in Edvard Radzinsky's "Conversations with Socrates" in 1975 was acclaimed by critics and made him one of the "most interesting and strongest actors of the contemporary scene." During the 1970s and 1980s, Dzhigarkhanyan appeared less frequently on stage and more frequently in films and became known to the wider Soviet public. Even with decreased number of appearances on stage, Dzhigarkhanyan's every role became an object of discussion. The finest roles from this period include Big Daddy in "Cat on a Hot Tin Roof" by Tennessee Williams, Lord Bothwell in Robert Bolt's "Vivat! Vivat Regina!", Nero in Edvard Radzinsky's "Theater in the Time of Nero and Seneca" and others.