  We define a general notion of Gel'fand-Tsetlin algebras in the framework of
inductive limit of the family semisimple star-algebras and the notion of
genralized conditional expectations. The inmverse limit of such family with
respect to generalized expectation is bimodule over inductive limit. The most
important examples conserned to inductive families of group algebras of
classical series of the discrete and continuous groups. I start from some
remarks about distinguished role of I.M.Gel'fand's conceptions in whole area.
