  We proved in a previous article that the bar complex of an E-infinity algebra
inherits a natural E-infinity algebra structure. As a consequence, a
well-defined iterated bar construction B^n(A) can be associated to any algebra
over an E-infinity operad. In the case of a commutative algebra A, our iterated
bar construction reduces to the standard iterated bar complex of A. The first
purpose of this paper is to give a direct effective definition of the iterated
bar complexes of E-infinity algebras. We use this effective definition to prove
that the n-fold bar complex B^n(A) admits an extension to categories of
algebras over E_n-operads. Then we prove that the n-fold bar complex determines
the homology theory associated to a category of algebras over E_n-operads. For
n infinite, we obtain an isomorphism between the homology of an infinite bar
construction and the usual Gamma-homology with trivial coefficients.
