  The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS
hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when
matrix entries are bosonic and fermionic unconstrained N=2 superfields is
proposed. This is done by exhibiting the corresponding matrix Lax--pair
representation in terms of N=2 unconstrained superfields. It is demonstrated
that when matrix entries are chiral and antichiral N=2 superfields, it
reproduces the N=2 chiral matrix (k|n,m)-GNLS hierarchy, while in the scalar
case, k=1, it is equivalent to the N=2 supersymmetric multicomponent hierarchy
(J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example --the N=2
unconstrained (1|1,0)--GNLS hierarchy-- and its reduction to the N=2
supersymmetric {\alpha}=1 KdV hierarchy are discussed in more detail, and its
rich symmetry structure is uncovered.
