  The data of cosmic ray NEVOD-DECOR experiment on the investigation of
inclined muon bundles for a long time period (May 2012 - March 2021) are
presented. The analysis showed that the observed intensity of muon bundles at
primary cosmic ray energies of about 1 EeV and higher can be compatible with
the expectation in frame of widely used hadron interaction models only under
the assumption of an extremely heavy mass composition. This conclusion is
consistent with data of several experiments on investigations of muon content
in air showers, but contradicts the available fluorescence data on Xmax which
favor a light mass composition at these energies. In order to clarify the
nature of the "muon puzzle", investigations of the muon bundle energy deposit
in the detector material were carried out. For the first time, experimental
estimates of the average energy of muons in the bundles of inclined air showers
initiated by primary particles with energies from 10 to 1000 PeV have been
obtained.
