  Hardening of cosmic proton- and nuclei-spectra is explained by using the
gluon condensation (GC) model, which states that a large amount of gluons in
proton may condense near the high energy threshold. The results present the
GC-effect as common origin of a series of anomalous astrophysical phenomena
including the broken power-law in gamma-ray spectra, the excess in positron-
and electron-spectra and hardening of proton- and nuclei-spectra.
