  Constrained KP and super-KP hierarchies of integrable equations (generalized
NLS hierarchies) are systematically produced through a Lie algebraic AKS-matrix
framework associated to the homogeneous grading. The role played by different
regular elements to define the corresponding hierarchies is analyzed as well as
the symmetry properties under the Weyl group transformations. The coset
structure of higher order hamiltonian densities is proven.\par For a generic
Lie algebra the hierarchies here considered are integrable and essentially
dependent on continuous free parameters. The bosonic hierarchies studied in
\cite{{FK},{AGZ}} are obtained as special limit restrictions on hermitian
symmetric-spaces.\par In the supersymmetric case the homogeneous grading is
introduced consistently by using alternating sums of bosons and fermions in the
spectral parameter power series.\par The bosonic hierarchies obtained from
${\hat {sl(3)}}$ and the supersymmetric ones derived from the $N=1$
affinization of $sl(2)$, $sl(3)$ and $osp(1|2)$ are explicitly constructed.
\par An unexpected result is found: only a restricted subclass of the $sl(3)$
bosonic hierarchies can be supersymmetrically extended while preserving
integrability.
