We present the interpretation of the muon and scintillation signals of ultra-high-energy air showers observed by AGASA and Yakutsk extensive air shower array experiments. We consider case-by-case ten highest energy events with known muon content and conclude that at the 95% confidence level (C.L.) none of them was induced by a primary photon. Taking into account statistical fluctuations and differences in the energy estimation of proton and photon primaries, we derive an upper limit of 36% at 95% C.L. on the fraction of primary photons in the cosmic-ray flux above 10^20 eV. This result disfavors the Z-burst and superheavy dark-matter solutions to the GZK-cutoff problem.
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