Based on the theories of the ring resonators and the directional coupler,the theoretical models of the microfiber double-knot resonator with a serial structure and the microfiber double-knot resonator with a parallel structure were proposed,the mathematic expressions between the output light field and the input one in the two resonators were deduced.The directions of the propagation and coupling in the two resonators were studied, the change rules of the transmission spectra under different diameter ratios of their two rings were analyzed.Numerical simulation indicates that the number of the transmission peaks of the microfiber double-knot resonator with a serial structure under the envelope of its transmission spectrum is equal to the diameter ratio of its two rings,the number of the transmission peaks of the microfiber double-knot resonator with a parallel structure increases with the increasing of the diameter ratio of its two rings and there is a narrower transmission peak per equal spacing peaks of the diameter ratio.The microfiber double-knot resonator with a serial structure for approximately equivalent diameters and the microfiber double-knot resonator with a parallel structure for a diameter ratio of approximate 2 were fabricated.The experimental transmission spectra show good agreements with the theoretical ones for each structure,indicating that the theoretical analysis is considerably correct.The microfiber double-knot resonator with a serial structure and that with a parallel structure for proper diameter ratios have significant applications in optical filters,miniature lasers,sensors,and so on.