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Uncertainties of the model energy spectra of secondary pi+- -mesons (and K+--mesons) at the most high energies of generation are discussed. In terms of the VENUS 4.12, DPMJET 2.55, QGSJET II-03 and SIBYLL 2.3 models computer simulations of energy spectra of the atmospheric vertical muons induced by primary cosmic particles with various fixed energies in interval 10**2-����10**7 GeV had been carried out by Monte-Carlo method. These spectra are integrated with the help of the contemporary spectra of nucleons of the primary radiation. Results of simulations are compared with the contemporary data on the atmospheric vertical muon flux obtained in various scientific collaborations. Comparison shows that all models underestimate production of secondary pi+--mesons (and K+--mesons) by factor of approximately 2 at the most high energies at the vicinity of energy of the primary particle. This underestimation induces more rapid development of extensive air showers in the atmosphere and results in uncertainties in estimates of parameters of hadron interactions at the most high energies. 1