The term 'BOTH BEGLEYS' refers to the father-son acting duo of Henry and Ed Begley Jr. Henry Begley was an American actor who appeared in films such as 'The Unsinkable Molly Brown' and 'The Sting'. His son, Ed Begley Jr., is also an actor who has appeared in films such as 'A Mighty Wind' and 'St. Elsewhere'. He is also an environmental activist and has won several awards for his work. The crossword solution for this term is EDS, which stands for Edward and Henry Begley Sr.