  We find the explicit form of the basic monodromy operators for the case of
the quantum group $\mathrm U_q(\mathcal L(\mathfrak{sl}_3))$. Expressions for
the quantum Casimir elements of the quantum groups $\mathrm
U_q(\mathfrak{gl}_3)$ and $\mathrm U_q(\mathfrak{sl}_3)$ are obtained as a
by-product.
