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We discuss the "generalized fluctuation-dissipation relations (theorems)" for the first time suggested by us in 1977-1984 as statistical-thermodynamical consequences of time symmetry (reversibility) of microscopic dynamics. It is shown, in particular, that our old results in essence contain, as alternative formulations or special cases, various similar relations (including the "fluctuation theorems") what appeared in 1997 and later. PACS 05.20.-y, 05.40.-a, 05.70.-a