  A homogeneous symmetric structure on an associative superalgebra A is a
non-degenerate, supersymmetric, homogeneous (i.e. even or odd) and associative
bilinear form on A. In this paper, we show that any associative superalgebra
with non null product can not admit simultaneously even-symmetric and
odd-symmetric structure. We prove that all simple associative superalgebras
admit either even-symmetric or odd-symmetric structure and we give explicitly,
in every case, the homogeneous symmetric structures. We introduce some notions
of generalized double extensions in order to give inductive descriptions of
even-symmetric associative superalgebras and odd-symmetric associative
superalgebras. We obtain also an other interesting description of odd-symmetric
associative superalgebras whose even parts are semi-simple bimodules without
using the notions of double extensions.
