The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N = 2 supersymmetric (n, m)-GNLS hierarchy are constructed in terms of N = 2 superfields in two different superfield bases with local evolution equations. Their bosonic limits are studied in detail. New local and nonlocal bosonic and fermionic integrals both for the N = 2 supersymmetric (n, m)-GNLS hierarchy and its bosonic counterparts are derived. As an example, in the n=1, m=1 case, the algebra and the symmetry transformations for some of them are worked out and a rich N=4 supersymmetry structure is uncovered.Recently there has been an intense research activity on N=2 supersymmetric integrable hierarchy. Basically this stems from the interest spurred by the ordinary integrable hierarchies and their relation to the 2D gravity and N=2 supersymmetric models representing superstring vacua. Although an analysis of this connection for the N=2 supersymmetric integrable hierarchies is still lacking, it is nevertheless a fact that the latter hierarchies have extremely rich and interesting structures. In [1] a large class of such hierarchies was introduced: the N = 2 supersymmetric (n, m) Generalized Nonlinear Schrödinger (GNLS) hierarchies. They were subsequently studied in a number of other papers, [2,3,4,5,6].The goal of the present letter is to fill a gap in our knowledge of these hierarchies by analyzing their Hamiltonian structures. In particular we produce here the first two Hamiltonian structures and the relevant recursion operators, as well as related local and non-local conserved charges, in two different superfield representations which possess local flow equations.Let us start with a short summary of the main facts concerning the N = 2 supersymmetric (n, m)-GNLS hierarchy [1, 6] which will be useful in what follows.The Lax operator of the N = 2 supersymmetric (n, m)-GNLS hierarchy has the following form