  The super Moyal-Lax representation and the super Moyal momentum algebra are
introduced and the properties of simple and extended supersymmetric integrable
models are systematically investigated. It is shown that, much like in the
bosonic cases, the super Moyal-Lax equation can be interpreted as a Hamiltonian
equation and can be derived from an action. Similarly, we show that the
parameter of non-commutativity, in this case, is related to the central charge
of the second Hamiltonian structure of the system. The super Moyal-Lax
description allows us to go to the dispersionless limit of these models in a
singular limit and we discuss some of the properties of such systems.
