  We construct a Darboux transformation of a general $su(3)$-valued spin system
called the $\Gamma$-spin system. Using this Darboux transformation we derive a
recursive formula for the soliton solutions of this spin system. Then using
these results we present explicit expressions for the 1-soliton solution of the
coupled $su(2)$-valued spin systems, namely, of the coupled M-LIII equation.
