  The structure of octonionic bimodules is formulated in this paper. It turns
out that every octonionic bimodule is a tensor product, the category of
octonionic bimodules is isomorphic to the category of real vector spaces. We
show that there is also a real part structure on octonionic bimodules similar
to the quaternion case. Different from the quaternion setting , the octonionic
bimodule sturcture is uniquely determined by its left module structure and
hence the real part can be obtained only by left multiplication. The structure
of octonionic submodules generated by one element is more involved, which leads
to many obstacles to further development of the octonionic functional analysis.
We introduce a notion of cyclic decomposition to deal with this difficulty.
Using this concept, we give a complete description of the submodule generated
by one element in octonionic bimodules. This paper clears the barrier of the
structure of $\O$-modules for the later study of octonionic functional
analysis.
