Three methods for calculating the transport of energetic protons and hydrogen atoms within the Earth's atmosphere are compared. The methods are (1) a Monte Carlo (MC) simulation, (2) a discrete energy loss solution to the linear transport equations, and (3) a continuous slowing-down approximation (CSDA). In the calculations performed, all three models use the same cross sections, three-component (N2, O2, O) neutral atmosphere, and incident isotropic Maxwellian proton fluxes of various characteristic energies (1--20 keV). To ensure that all three methods include the same physical processes, the effects of magnetic mirroring and the lateral spreading of particles are ''turned off'' in the MC simulations as these processes are not included in the present linear transport or CSDA models. A variety of quantities are calculated and compared including energy deposition rates, eV/ion pair, hemispherically averaged differential fluxes of protons and H atoms, energy integrated differential fluxes, and total proton and H atom fluxes. The agreement between all three models is excellent except at the lowest altitudes. Apart from these altitudes, the differences that do exist are small compared to the errors that generally result from poorly known inputs and compared to the typical errors quoted for geophysical observations. The altitudes where the results do differ significantly are where the proton and H-atom-fluxes are severely attenuated and are below the altitudes where the bulk of the energy deposition and ionization takes place. The success of these comparisons suggests that our ability to model actual observations is presently limited by uncertainties in cross sections and the lack of suitable observations rather than our ability to solve the equations that describe the known physics of proton-H atom transport. ¿ American Geophysical Union 1996