The study of spatial dispersion in electromagnetic wave propagation in random media is approached via the quasi-crystalline approximation in the framework of multiple-scattering theory. Longitudinal and transverse permittivity kernels are obtained explicitly by using a simplified resonant model for the T-matrix of the scatterers. The transverse dispersion equation is solved numerically for all its frequency-dependent solutions in a given domain of the complex plane. The physical meaning of these solutions is discussed.