The rational meromorphic functions on $\mathbb{C}\backslash\mathbb{R}$ are studied. We consider the some classes of one, as generalized Nevanlinna $\mathbf{N}_{\kappa}$ and Stieltjes $\mathbf{N}_{\kappa}^{k}$ classes. By Euclidean algorithm, we can find indices $\kappa$ $k$, i.e. determine which class function belongs to $\mathbf{N}_{\kappa}^{k}$.