Understanding the physical processes involved in the propagation of cosmic rays in the intergalactic media is one of the biggest problems in astrophysics today. It is an important topic because one first tries to identify the sources and later to understand the physical processes that occur when the particles are accelerated to ultra-high energies (E> E > 1018 18 eV). And because cosmic rays are charged particles, they are deflected in the existing magnetic fields as they propagate to Earth, making it very difficult to correlate their direction of arrival with astrophysical sources. Moreover, cosmic rays consist mainly of atomic nuclei interacting with the cosmic microwave background (CMB) and the extragalactic background light (EBL) during their propagation, and a significant part of their energy is consumed in these processes (for a proton with E 1021 21 eV, its energy is approximately halved over a distance of 20 Mpc). In this article, we describe the main processes between background photons and ultrahigh-energy cosmic rays. We have also used the equations for comparison with the most commonly used programme in this field to illustrate the physical processes addressed. We conclude that the result of the equations leads to well-established results in the field, such as the importance of EBL for the process of photodesintegration (Allard, 2012). (c) 2024 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.