  Unique twistor--like Lorentz harmonic formulation for all N=1 supersymmetric
extended objects (super-p-branes) moving in the space--time of arbitrary
dimension D (admissible for given $p$) are suggested. The equations of motion
are derived, explicit form of the \kappa-symmetry transformations is presented
and the classical equivalence to the standard formulation is proved.
  The cases with minimal world--sheet dimensions $p=1,2$, namely of D=10
heterotic string and D=11 supermembrane, are considered in details. In
particular, the explicit form of irreducible \kappa-symmetry transformations
for D=11 supermembrane is derived.
