  In the present paper we obtain some integrable generalisations of the Toda
system generated by flat connection forms taking values in higher ${\bf
Z}$--grading subspaces of a simple Lie algebra, and construct their general
solutions. One may think of our systems as describing some new fields of the
matter type coupled to the standard Toda systems. This is of special interest
in nonabelian Toda theories where the latter involve black hole target space
metrics. We also give a derivation of our conformal system on the base of the
Hamiltonian reduction of the WZNW model; and discuss a relation between abelian
and nonabelian systems generated by a gauge transformation that maps the first
grading description to the second. The latter involves grades larger than one.
