Gauge invariant formulation of Toda and KdV systems in extended superspace

We give a gauge invariant formulation of N = 2 supersymmetric abelian Toda field equations in N = 2 superspace. Superconformal invariance is studied. The conserved currents are shown to be associated with Drinfeld - Sokolov type gauges. The extension to non-abelian N = 2 Toda equations is discussed. Very similar methods are then applied to a matrix formulation in N = 2 superspace of one of the N = 2 KdV hierarchies.