  A linear system, which generates a Moyal-deformed two-dimensional soliton
equation as integrability condition, can be extended to a three-dimensional
linear system, treating the deformation parameter as an additional coordinate.
The supplementary integrability conditions result in a first order differential
equation with respect to the deformation parameter, the flow of which commutes
with the flow of the deformed soliton equation. In this way, a deformed soliton
hierarchy can be extended to a bigger hierarchy by including the corresponding
deformation equations. We prove the extended hierarchy properties for the
deformed AKNS hierarchy, and specialize to the cases of deformed NLS, KdV and
mKdV hierarchies. Corresponding results are also obtained for the deformed KP
hierarchy. A deformation equation determines a kind of Seiberg-Witten map from
classical solutions to solutions of the respective `noncommutative' deformed
equation.
