  By using graded (super) Lie algebras, we can construct noncommutative
superspace on curved homogeneous manifolds. In this paper, we take a flat limit
to obtain flat noncommutative superspace. We particularly consider $d=2$ and
$d=4$ superspaces based on the graded Lie algebras $osp(1|2)$, $su(2|1)$ and
$psu(2|2)$. Jacobi identities of supersymmetry algebras and associativities of
star products are automatically satisfied. Covariant derivatives which commute
with supersymmetry generators are obtained and chiral constraints can be
imposed. We also discuss that these noncommutative superspaces can be
understood as constrained systems analogous to the lowest Landau level system.
