We use and extend our previously published physical model of low-energy particle fluxes in the Earth's radiation belts [Boscher et al., 1998> to study four components of the temporal variations of radiation belt particle fluxes: the secular variation, related to that of the Earth's magnetic field; the solar cycle modulation; the magnetic storm effects; and the solar proton events. Our previous proton model, initially developed for equatorially mirroring low-energy particles, has been extended to higher energies in order to reproduce (1) the solar cycle influence on very high energy particles (around 100 MeV) at low altitudes and (2) the effects induced by strong active periods on protons with energies between 1 and 50 MeV. The good agreement found between our model results and observations shows that our physical model can be a safe contribution to the future development of engineering models that will be able to reproduce both the long-term variations of trapped proton fluxes (to define mission specifications) and short-term fluctuations (to understand in-flight satellite anomalies). ¿ 1999 American Geophysical Union