Recent development in the optical scintillation theory has been adapted to the ionospheric geometry in order to study the ionospheric scintillation phenomenon in the presence of multiple scattering. Under approximations well satisfied in typical ionospheres for a frequency above about 20 MHz, the first through fourth moment equations have been derived and some analytic solutions given. The fourth moment equation has also been solved numerically. The numerical results show clearly the occurrence of focussing and saturation phenomena. In this paper the new multiple-scatter effects are emphasized.