  We present two different hamiltonian extensions of the Degasperis - Procesi
equation to the two component equations. The construction based on the
observation that the second Hamiltonian operator of the Degasperis - Procesi
equation could be considered as the Dirac reduced Poisson tensor of the second
Hamiltonian operator of the Boussinesq equation. The first extension is
generated by the Hamiltonian operator which is a Dirac reduced operator of the
generalized but degenerated second Hamiltonian operator of the Boussinesq
equation. The second one is obtained by the N=2 supersymmetric extension of the
mentioned method. As the byproduct of this procedure we obatined the
Hamiltonian system of interacting equations which contains the Camassa - Holm
and Degasperis - Procesi equation.
