The processes are analyzed by which extremely relativistic protons lose energy under the conditions thought to apply in the central engines of active galactic nuclei. Analytic formulae are derived which permit the consequences of relativistic proton injection under a variety of conditions to be predicted. Different proton cooling mechanisms are compared for a power-law proton injection function and two types of background radiation spectra: power-law and power-law plus blackbody. The kinetic equations for neutrons and protons are examined, and it is shown how to calculate the energy distributions of primary gamma rays and escaping neutrons and neutrinos.