  We aim to show the importance of non-elastic excitation and deexcitation
processes in $\textrm{He}^{*}(n)+ \textrm{He}(1s^{2})$ collisions with the
principal quantum number $n \ge 3$ for helium-rich white dwarf atmospheres. We
compare the efficiencies of these processes with those of the known non-elastic
electron-$\textrm{He}^{*}(n)$ atom processes in the atmospheres of some DB
white dwarfs. We show that in significant parts of the considered atmospheres,
which contain weakly ionized layers (the ionization degree $\lesssim 10^{-3}$),
the influence of the studied atom-Rydberg atom processes on excited helium atom
populations is dominant or at least comparable to the influence of the
concurrent electron-$\textrm{He}^{*}(n)$-atom processes.
