Coupled-line ring hybrids (CRHs) are presented for arbitrary circumferences and for arbitrary power-division ratios. They each consist of three single transmission-line sections and a set of coupled transmission-line sections with or without two identical capacitances and contain most properties of the conventional ring hybrids. Therefore, they may be called general CRHs and can be designed for the frequency performance better than that of any other conventional one. By adopting the coupled-line sections, the 180° phase shift can be guaranteed, regardless of fabrication technologies, but three or four unknown variables more should be considered additionally, which results in a complicated derivation process. To make it simpler, two conditions of S11e=S22o and S22e=S11o, where S11 and S22 are scattering parameters, and the superscripts of e and o are meant as even- and odd-mode excitations, respectively, are newly employed. To verify the suggested theory, two prototypes were tested for the power-division ratios of 0 and -5 dB without and with capacitances, respectively. The measured results are in good agreement with the predicted ones, and the measured bandwidths with 15-dB return loss are 82.9 % and 97.65 % for the power-division ratios of 0 and -5 dB, respectively.