  We discuss the production of ultra high energy secondary protons by cosmic
ray primary nuclei propagating in the intergalactic space through Cosmic
Microwave Background (CMB) and Infrared (IR) radiations. Under the assumption
that only primary nuclei with a fixed atomic mass number $A_0$ are accelerated,
the spectrum of secondary protons is calculated. It is found that for all $A_0$
the diffuse flux of secondary protons starts to dominate over that of primary
nuclei at energy $E \sim (1 - 2)\times 10^{19}$ eV, and thus the standard
Greisen-Zatsepin -Kuzmin (GZK) cutoff is produced.
