We study two members of the multi-component AKNS hierarchy. These are
multi-NLS and multi-MKdV systems. We derive the Hirota bilinear forms of these
equations and obtain soliton solutions. We find all possible local and nonlocal
reductions of these systems of equations and give a prescription to obtain
their soliton solutions. We derive also $(2+1)$-dimensional extensions of the
multi-component AKNS systems.Comment: 19 page