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We predict the external radiation with a frequency half the frequency of alternating Josephson effect to appear when a constant voltage is applied to a quasicrystal–quasicrystal tunneling junction. Thus the phenomenon typical for superconductor–superconductor junctions can be realized for a non-superconducting object. The physical background for this possibility is the “critical” behavior of the wave functions in quasicrystals and electron scattering on a quasiperiodic potential. The effect opens an avenue for new applications of quasicrystals.