In the barrier mathod and.6 in. the method of centres one has to suppose that, a regldarity condition in fulfilied in order to excure that every aecrecation point of the solotions of the sequence of supporting problems selves the ,origira optimization problam.Varions conditions are used for regularity conditions in papers on the theory of barrier methods and methods of centres. We summarizo those different conditions and investigate their mutual relations. Moreover, it is shown that some well known regularity conditions of the Kcen-Tucker-theory are also regularity conditions in the sense considered here. The barrier method and the method of centres are represented in linear topological spaces.