  The processes of the generation of cosmogenic neutrons (cg-neutrons)
underground are considered. The neutrons produced by cosmic-ray muons in their
interactions with matter are called cosmogenic. Deep-inelastic
${\pi}A$-collisions of pions in muon-induced hadronic showers are mainly their
source at energies above 30 MeV. The characteristics of the energy spectrum for
the generation of cg-neutrons have been determined by invoking the additive
quark model of deep-inelastic soft processes and the mechanism for the
interactions of high-energy nucleons in a nucleus. The three-component shape of
the spectrum is explained, and the energy of the "knee" in the spectrum has
been found to depend on the mass number $A$. The peculiarities of
deep-inelastic ${\pi}A$-scattering lead to the conclusion that the spectrum of
cg-neutrons steepens sharply at energies above 1 GeV. The calculated
quantitative characteristics of the spectrum are compared with those obtained
in measurements.
