We now observe a new type of dynamical state in long Josephson junctions. Millimeter-wave irradiation in the frequency range ${\mathit{f}}_{\mathrm{ext}}$=62–77 GHz, was applied to a long junction biased in the flux-flow mode. Besides an ordinary flux-flow step satellite, flux-flow steps with voltage spacing corresponding to 2${\mathit{f}}_{\mathrm{ext}}$ were observed. The dependence of the amplitude of the satellite steps on external magnetic field and microwave power was measured. An explanation of the satellite steps as mixing products due to the microwave-assisted reflection of fluxons into antifluxons at the junction boundary is presented.

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