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The Josephson Flux-Flow Oscillator (FFO) has been used as an on chip local oscillator at frequencies up to 650 GHz. The FFO linewidth of about 1 MHz was measured in the resonant regime V<915 /spl mu/V for niobium-aluminum oxide-niobium tunnel junctions, while considerably larger values were reported at higher voltages. To overcome this fundamental linewidth broadening we propose a novel on chip Cherenkov radiation flux-flow oscillator (CRFFO). It consists of a long Josephson junction and a superconducting slow wave transmission line that modifies essentially the junction dispersion relation. Two SIS detectors are connected both to the long Josephson junction and the transmission line to evaluate available microwave power. The output power coming both from the long junction and the transmission line is estimated at different bias conditions.