Existing calculations of the total absorption coefficient are generally based on the assumption that all the primary radiation energy which is converted into Comptonscattered radiation escapes from the material without significant absorption. This paper extends this basic assumption to include fluorescent and annihilation radiation and bremsstrahlung, and new values of the photoelectric, Compton, pair production, and total absorption coefficients are determined in the energy range O� 01-100 MeV for hydrogen, nitrogen, oxygen, argon, aluminium, iron, lead, air, and water. For comparison purposes revised values of the total absorption coefficient, allowing for the Compton radiation energy loss only, are also determined for these materials, using the most recent data for the component coefficients.