We show that if a closed
n
n
-manifold
M
n
M^n
(
n
≥
3
)
(n\ge 3)
admits a structurally stable diffeomorphism
f
f
with an orientable expanding attractor
Ω
\Omega
of codimension one, then
M
n
M^n
is homotopy equivalent to the
n
n
-torus
T
n
T^n
and is homeomorphic to
T
n
T^n
for
n
≠
4
n\ne 4
. Moreover, there are no nontrivial basic sets of
f
f
different from
Ω
\Omega
. This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having codimension one orientable expanding attractors and contracting repellers on
T
n
T^n
,
n
≥
3
n\ge 3
.