Using a convection-diffusion theory, we give the first results from a four-dimensional model of electron and proton radiation belts. This work is based on the numerical solution of a convection-diffusion equation taking into account (1) for protons, the deceleration of protons by the free and bounded thermospheric and ionospheric electrons, the charge exchange loss process, radial and azimuthal transports, and (2) for electrons,the deceleration of electrons by the free and bounded electrons of the medium, pitch angle diffusion by Coulomb and wave-particle interactions, radial and azimuthal transport. This model allows for simulation of a magnetic storm effects by increasing convective electric field and injecting particles with keV range energies in the nightside region. Particles in the energy range 50--100 keV are created by acceleration of slower particles in the L=4 region. Four hours are needed for ring current formation. The calculated particle distribution at 6.6 Earth radii as well as at low altitude are in good agreement with those deduced from ATS 6 measurements (the drift echo is well reproduced at this altitude) and from statistical studies of the precipitation by the DMSP satellites, respectively.¿ 1997 American Geophysical Union