  We study the supersymmetric extensions of the Harry Dym hierarchy of
equations. We obtain the susy-B extension, the doubly susy-B extension as well
as the N=1 and the N=2 supersymmetric extensions for this system. The N=2
supersymmetric extension is particularly interesting, since it leads to new
classical integrable systems in the bosonic limit. We prove the integrability
of these systems through the bi-Hamiltonian formulation of integrable models
and through the Lax description. We also discuss the supersymmetric extension
of the Hunter-Zheng equation which belongs to the Harry Dym hierarchy of
equations.
