  The q-deformed algebra ${\rm so}'_q(r,s)$ is a real form of the q-deformed
algebra $U'_q({\rm so}(n,\mathbb{C}))$, $n=r+s$, which differs from the quantum
algebra $U_q({\rm so}(n,\mathbb{C}))$ of Drinfeld and Jimbo. We study
representations of the most degenerate series of the algebra ${\rm
so}'_q(r,s)$. The formulas of action of operators of these representations upon
the basis corresponding to restriction of representations onto the subalgebra
${\rm so}'_q(r)\times {\rm so}'_q(s)$ are given. Most of these representations
are irreducible. Reducible representations appear under some conditions for the
parameters determining the representations. All irreducible constituents which
appear in reducible representations of the degenerate series are found. All
$*$-representations of ${\rm so}'_q(r,s)$ are separated in the set of
irreducible representations obtained in the paper.
