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An X-band dual-frequency coaxial relativistic backward-wave oscillator (CRBWO) with sectioned slow-wave structures (SWSs) is presented and investigated in this paper. Through theoretical and numerical analysis and particle-in-cell (PIC) simulation, a combination generation of two stationary single-frequency regimes is selected as the operation regime of the two-section CRBWO, and a better understanding of the high-frequency characteristics of the system, including the unstable beam-wave interaction regions of each section and the operation mode of each section, is obtained. The PIC simulation results indicate that, with an electron beam of 500 kV and 8.7 kA guided by an axial magnetic field of 0.82 T, average power of 700 MW with power conversion efficiency up to 16.1% is obtained, and the two dominant frequencies are 10.06 and 10.49 GHz, respectively. Theoretical analysis indicates that the operation modes of the two sections are TM01 modes.