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A dual-mode open-loop slotline resonator with a centre-loaded stub is proposed. The loaded stub is used to excite non-degenerate modes, that is, the even and odd modes. Distinct characteristics of this dual-mode resonator are investigated by using even-odd mode analysis. Also, equivalent circuit models for non-degenerate modes are given to determine the resonance conditions and the location of transmission zero. Then, two novel approaches for designing dual-mode dual-band bandpass filters are presented. One approach consists of simple microstrip feedlines and two embedded open-loop slotline resonators for single substrate configuration. The other is composed by using dual-mode open-loop resonators in the form of microstrip and slotline structures on a single substrate. A microstrip invert L-shape feeding structure is employed to simultaneously feed the microstrip and slotline resonator on different layers for broadside coupling. Both of them provide sufficient degrees of freedom to control the centre frequencies and fractional bandwidths of both passbands independently. The two filters are designed, fabricated and measured. A good agreement between the simulation and measurement verifies the validity of this design methodology.