Evidence for superluminal radiation in γ-ray burst (GRB) spectra is pointed out. The spectral maps of GRB 941017, GRB 990123, and GRB 990104 are analyzed. The superluminal radiation modes are generated by the shock-heated ultra-relativistic source plasma. The tachyonic radiation field is a real Proca field with negative mass-square, coupled to the electron gas by a frequency-dependent fine-structure constant. At GeV energies, the coupling constant approaches a limit value, so that the radiation

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... field is minimally coupled to the electron current. In the soft γ-ray band, the interaction with the GRB plasma becomes nonlocal, due to the varying coupling strength depending on the energy of the radiated modes. The spectral fitting with tachyonic flux densities generated by nonlocal plasma currents is explained. Estimates of the tachyonic luminosity, temperature, and internal energy of the electronic source plasma are obtained from the spectral fits.