Dear colleagues, my new preprint is now available in Category Theory section of http://au.arxiv.org/ You also can download it from my home page http://www.math.mq.edu.au/~mbatanin/papers.html the .ps file is preferable because it contains all the pictures. Some of the pictures are missing from dvi file. Below is the abstract Title: The Eckmann-Hilton argument, higher operads and E_n-spaces Authors: M.A.Batanin Comments: 52 pages, 19 figures Subj-class: Category Theory; Algebraic Topology MSC-class: 18D05, 18D50, 55P48 \\ The classical Eckmann-Hilton argument shows that two monoid structures on a set, such that one is a homomorphism for the other, coincide and, moreover, the resulting monoid is commutative. This argument immediately gives a proof of the commutativity of the higher homotopy groups. A reformulation of this argument in the language of higher categories is: suppose we have a one object, one arrow 2-category, then its Hom-set is a commutative monoid. A similar argument due to A.Joyal and R.Street shows that a one object, one arrow tricategory is `the same' as a braided monoidal category. In this paper we extend this argument to arbitrary dimension. We demonstrate that for an n-operad A in the author's sense there exists a symmetric operad S^n(A) called the n-fold suspension of A such that the category of one object, one arrow , . . . , one (n-1)-arrow algebras of A is equivalent to the category of algebras of S^n(A). Moreover, under some mild conditions, we present an explicit formula for S^n(A) which involves taking the colimit over a remarkable categorical E_n-operad. In the case, where A is contractible in an appropriate sense, this formula provides us with an action of the E_n-operad on algebras of S^n(A). \\ 30-Jul-2002 18:56:10 -0300,1039;000000000000-00000025