Archival EAS-MSU data are searched for anomalous muonless events which may be caused by primary gamma rays with energies between 10 15 eV and 10 18 eV. We consider a refined sample of high-quality data and confirm the previously reported detection of a non-zero gamma-ray flux at ∼ 5 × 10 16 eV with a similar flux value but at somewhat lower statistical significance, corresponding to a depletion of the sample. We present upper limits on the flux below and above these energies, including the first constraints in the range 10 17 − 10 18 eV never studied by any other experiment.Searches for primary gamma rays in the extensive air shower (EAS) data have continued since 1960s (see e.g. Ref.[1] and, for a recent review, Ref.[2]) but started to attract a special attention after the recent announcement of the discovery of high-energy astrophysical neutrinos by the IceCube collaboration [3,4,5]. Indeed, in conventional scenarios, the high-energy neutrinos are produced in decays of charged pions, while accompanying neutral pions decay into photons (see e.g. Refs. [6,7,8,9] for more detailed discussions). Discovery of the neutrinos thus gives a hope to find the accompanying photons.One of the most elaborated methods to discriminate primary gamma rays is to search for air showers with low muon content because secondary muons are produced in hadronic interactions while the photon-induced EAS are mostly electromagnetic. A recent study of EAS-MSU events with estimated number of particles N e > 2 × 10 7 has revealed [10] an excess of muonless events compatible with non-zero primary gamma-ray flux at energies 50 PeV. The present work verifies the reported value of the flux with a refined sample of high-quality data and extends the N e range to demonstrate a coherent picture of the photon-flux measurements and upper limits in a wide energy band between ∼ 5 PeV and ∼ 500 PeV.The EAS-MSU experiment [11] and the analysis method [10] are described in detail in previous works. For the present study, events with the reconstructed number of particles N e > 10 6 and zenith angles θ < 30• , detected in 1982-1990, are selected. Muons with energies > 10 GeV were recorded by the central muon detector of 36.4 m 2 area. For air showers with N e > 10 7 , the triggering and selection systems have been described in 1) e-mail: st@ms2.inr.ac.ru Ref. [10]. At lower N e , the central selection system was used, based on a subset of 7 scintillator detectors; the central one, of 1 m 2 area, and 6 peripheric ones, each of 0.5 m 2 area, located at ∼ 60 m from the central one. The trigger corresponds to a simultaneous (within the time gate of 500 ns) firing of the central detector (with the threshold of 1 relativistic particle) and of at least two of peripheric ones (whose thresholds were set at the level of 1/3 of a relativistic particle). It is required that the 3 detectors do not lay on a straight line so that the determination of the EAS arrival direction is possible. The time resolution of the system is ∼ 5 ns, which determines the precision of ≤ 3• in...