  In the present paper we obtain some integrable generalisations of the
continuous Toda system generated by a flat connection form taking values in
higher grading subspaces of the algebra of the area--preserving diffeomorphism
of the torus $T^2$, and construct their general solutions. The grading
condition which we use here, imposed on the connection, can be realised in
terms of some holomorphic distributions on the corresponding homogeneous
spaces.
