We formulate a conjecture for the three different Lax operators that d
escribe the bosonic sectors of the three possible N = 2 supersymmetric
integrable hierarchies with N = 2 super-W-n second Hamiltonian struct
ure. We check this conjecture in the simplest cases, then we verify it
in general in one of the three possible supersymmetric extensions, To
this end we construct the N = 2 supersymmetric extensions of the Gene
ralized Non-Linear Schrodinger hierarchy by exhibiting the correspondi
ng super Lax operator. To find the correct Hamiltonians we are led to
a new definition of super-residues for degenerate N = 2 supersymmetric
pseudo-differential operators. We have found a new non-polynomials Mi
ura-like realization for N = 2 superconformal algebra in terms of two
bosonic chiral-anti-chiral free superfields.