2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94396We construct the matrix generalization of the N=2 supersymmetric GNLS hierarchies. This is done by exhibiting the corresponding matrix super Lax operators in terms of N=2 superfields in two different superfield bases. We present the second Hamiltonian structure and discrete symmetries. We then extend our discussion by conjecturing the Lax operators of different reductions of the N=2 supersymmetric matrix KP hierarchy and discuss the simplest examples.13 pages, Latex, one reference addedExactly Solvable and Integrable SystemsHigh Energy Physics - Theorytext