  The present paper is dedicated to integrable models with Mikhailov reduction
groups $G_R \simeq \mathbb{D}_h.$ Their Lax representation allows us to prove,
that their solution is equivalent to solving Riemann-Hilbert problems, whose
contours depend on the realization of the $G_R$-action on the spectral
parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with
$\mathbb{D}_h$ symmetries are presented.
