  The evolution of the muon content of very high energy air showers (EAS) in
the atmosphere is investigated with data of the KASCADE-Grande observatory. For
this purpose, the muon attenuation length in the atmosphere is obtained to
$\Lambda_\mu = 1256 \, \pm 85 \, ^{+229}_{-232}(\mbox{syst})\, \mbox{g/cm}^2$
from the experimental data for shower energies between $10^{16.3}$ and
$10^{17.0} \, \mbox{eV}$. Comparison of this quantity with predictions of the
high-energy hadronic interaction models QGSJET-II-02, SIBYLL 2.1, QGSJET-II-04
and EPOS-LHC reveals that the attenuation of the muon content of measured EAS
in the atmosphere is lower than predicted. Deviations are, however, less
significant with the post-LHC models. The presence of such deviations seems to
be related to a difference between the simulated and the measured zenith angle
evolutions of the lateral muon density distributions of EAS, which also causes
a discrepancy between the measured absorption lengths of the density of shower
muons and the predicted ones at large distances from the EAS core. The studied
deficiencies show that all four considered hadronic interaction models fail to
describe consistently the zenith angle evolution of the muon content of EAS in
the aforesaid energy regime.
