  By making use of the data on the total signal and on the muon component of
the air showers detected by the Yakutsk array, we analyze, in the frameworks of
the recently suggested event-by-event approach, how large the fraction of
primary gamma-rays at ultra-high energies can be. We derive upper limits on the
photon fraction in the integral flux of primary cosmic rays. At the 95%
confidence level (CL), these limits are 22% for primary energies E_0>4\cdot
10^{19}eV and 12% for E_0>2\cdot 10^{19}eV. Despite the presence of muonless
events, the data are consistent with complete absence of photons at least at
95% CL. The sensitivity of the results to systematic uncertainties, in
particular to those of the energy determination for non-photon primaries, is
discussed.
