  The extended N=2 supersymmetric Camasa - Holm equation is presented. It is
accomplishe by formulation the supersymmeytric version of the Fuchssteiner
method. In this framework we use two supersymmetric recursion operators of the
N=2, $\alpha=-2,4$ Korteweg - de Vries equation and constructed two different
version of the supersymmetric Camassa - Holm equation. The bosonic sector of
N=2, $\alpha=4$ supersymmetric Camassa - Holm equation contains two component
generalization of this equation considered by Chen, Liu and Zhang and as a
special case two component generalized Hunter - Saxton equation considered by
Aratyn, Gomes and Zimerman, As a byproduct of our analysis we defined the N=2
supersymmetric Hunter - Saxton equation. The bihamiltonian structure is
constructed for the supersymmetric N=2, $\alpha=4$ Camassa - Holm equation.
