  We present a superspace formulation of N=1 eleven-dimensional supergravity
with no manifest local Lorentz covariance, which we call teleparallel
superspace. This formulation will be of great importance, when we deal with
other supergravity theories in dimensions higher than eleven dimensions, or a
possible formulation of noncommutative supergravity. As an illustrative
example, we apply our teleparallel superspace formulation to the case of N=1
supergravity in twelve-dimensions. We also show the advantage of teleparallel
superspace as backgrounds for supermembrane action.
