  We study MNLS related to the D.III-type symmetric spaces. Applying to them
Mikhailov reduction groups of the type $\mathbb{Z}_r\times \mathbb{Z}_2$ we
derive new types of 2-component NLS equations. These are {\bf not}
counterexamples to the Zakharov-Schulman theorem because the corresponding
interaction Hamiltonians depend not only on $|q_k|^2$, but also on $q_1q_2^*
+q_1^* q_2$.
