  We analyse the dynamics of an open membrane, both for the free case and when
it is coupled to a background three-form, whose boundary is attached to
$p$-branes. The role of boundary conditions and constraints in the Nambu-Goto
and Polyakov formulations is studied. The low-energy approximation that
effectively reduces the membrane to an open string is examined in detail.
Noncommutative features of the boundary string coordinates, where the
cylindrical membrane is attached to the D$p$-branes, are revealed by algebraic
consistency arguments and not by treating boundary conditions as primary
constraints, as is usually done. The exact form of the noncommutative algebra
is obtained in the low-energy limit.
