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It is shown that, three different Lax operators in the Dym hierarchy, producethree generalized coupled Harry Dym equations. These equations transform, viathe reciprocal link, to the coupled two-component KdV system. The firstequation gives us known integrable two-component KdV system while the secondreduces to the known symmetrical two-component KdV equation. The last onereduces to the Drienfeld-Sokolov equation. This approach gives us new Laxrepresentation for these equations.

Two-Component Coupled KdV Equations and its Connection with the Generalized Harry Dym Equation