We study SU(n) N=1 supersymmetric Chern-Simons systems in 2+1 dimensio
ns with and without a Maxwell term. Fixing the potential in a specific
way, the supersymmetry is extended to N=2 which leads to a system wit
h nontopological soliton solutions. The central charge of the extended
supersymmetry is calculated and self-dual equations for the backgroun
d fields are derived.