  It is shown that, three different Lax operators in the Dym hierarchy, produce
three generalized coupled Harry Dym equations. These equations transform, via
the reciprocal link, to the coupled two-component KdV system. The first
equation gives us known integrable two-component KdV system while the second
reduces to the known symmetrical two-component KdV equation. The last one
reduces to the Drienfeld-Sokolov equation. This approach gives us new Lax
representation for these equations.
