Who's Who in the Theatre by 
Notable Names in American Theatre by 
Famous Actors and Actresses on the American Stage by 
Notable Women in the American Theatre by 
American Women Stage Directors of the Twentieth Century by 
Contemporary Black American Playwrights and Their Plays by 
African American Dramatists by 
Stage Deaths by Full text obituaries of notable persons can also be found by searching historical newspaper indexes, including The New York Times, The Brooklyn Eagle, The New York Tribune, and The Baltimore African-American.
Nexis Uni is a good source for obituaries for those who have died more recently.
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British and Irish Dramatists Since World War II by 
Twentieth-Century American Dramatists by 
French Dramatists, 1789-1914 by 