We present analytic solutions for near equatorially mirroring protons of energies E?5--100 MeV at the lower edge of the radiation belt (L?1.25), based upon Crand-injection and time-varying energy losses. The proton spectral shape is essentially determined by Crand, whereas the ambient atmosphere controls the anisotropy and the spatial and temporal variations of the flux. The experimental data of Fischer et al. (1977) are used to check the results. Above L=1.25, radial diffusion gives rise to an enhancement of the flux, an increase of the anisotropy and a change of the energy spectrum. By means of perturbation methods, we show that the observed modifications of the energy spectrum require diffusion coefficients of the form DLL &agr; &mgr;-r with r>1.