A 2 - Component or N=2 Supersymmetric Camassa - Holm Equation

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.