Theatres went dark at 8 p.m. on Thursday in memory of Durning and will do so again at 8 p.m. today for Klugman.
Durning, who died Monday at 89, was a Tony Award-winner for his performance as Big Daddy in the 1990 revival of Cat on a Hot Tin Roof.
He also appeared in the original 1972 production of That Championship Season and a 1996 revival of Inherit the Wind.
His role in the 1983 film adaptation of the stage musical Best Little Whorehouse in Texas brought him one of this two Academy Award nominations.
Klugman, who died Monday at 90, received a Tony nomination for the original 1959 production of Gypsy, in which he played Herbie.
He replaced Walter Matthau as Oscar Madison in the original Broadway run of The Odd Couple in 1965 before going on to portray that character in the TV comedy adaptation.
His final appearance on Broadway was in 1997 in a revival of The Sunshine Boys with Odd Couple co-star Tony Randall.
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