Interconnection between polyadic systems and binary ones has been one of the main areas of interest POST , THURSTON. First constructions were confined to building some special polyadic (mostly ternary CERTAINE , LEHMER) operations on elements of binary groups MILLER, LEHMER, CHUNIKHIN . The very special form of n-ary multiplication in terms of binary multiplication and a special mapping as a chain formula was found in HOSSZ´ U  and GLUSKIN [1964, 1965]. A theorem which claims that any n-ary multiplication can be presented in this form is called a Hossz´u-Gluskin theorem (for review see DUDEK AND GŁAZEK , GAL’MAK ). A concise and clear proof of the Hossz´u-Gluskin chain formula was presented in SOKOLOV. In this paper we give a new form of the standard Hossz´u-Gluskin theorem in terms of polyadic powers. Then we show that the Hossz´u-Gluskin chain formula is not unique and can be generalized (“deformed”) using a parameter q which takes special integer values. We present the invariance version of the “q-deformed” analog of the Hossz´uGluskin theorem and consider examples. A “q-deformed” homomorphism theorem is also given.