The kinetics of the formation and reaction of hydrogen peroxide in the long time γ- radiolysis of water is examined using a combination of experiment with model calculations. Escape yields of hydrogen peroxide on the microsecond time scale are easily measured with added radical scavengers even with substantial amounts of initial added hydrogen peroxide. The γ-radiolysis of aqueous hydrogen peroxide solutions without added radical scavengers reach a steady state limiting concentration of hydrogen peroxide with increasing dose, and that limit is directly proportional to the initial concentration of added hydrogen peroxide. The dose necessary to reach that limiting hydrogen peroxide concentration is also proportional to the initial concentration, but dose rate has a very small effect. The addition of molecular hydrogen to aqueous solutions of hydrogen peroxide leads to a decrease in the high dose limiting hydrogen peroxide concentration that is linear with the initial hydrogen concentration, but the amount of decrease is not stoichiometric. Proton irradiations of solutions with added hydrogen peroxide and hydrogen are more difficult to predict because of the decreased yields of radicals; however, with a substantial increase in dose rate there is a sufficient decrease in radical yields that hydrogen addition has little effect on hydrogen peroxide decay.