  We develop a pseudo-differential approach to the N=2 supersymmetric
unconstrained matrix (k|n,m)-Generalized Nonlinear Schroedinger hierarchies and
prove consistency of the corresponding Lax-pair representation
(nlin.SI/0201026). Furthermore, we establish their equivalence to the
integrable hierarchies derived in the super-algebraic approach of the
homogeneously-graded loop superalgebra sl(2k+n|2k+m)\otimes
C[{lambda},{lambda}^{-1}] (nlin.SI/0206037). We introduce an unconventional
definition of N=2 supersymmetric strictly pseudo-differential operators so as
to close their algebra among themselves.
