The alpha-dispersion amplitude of suspensions of colloidal particles is usually calculated from the low-frequency asymptotic of the frequency-dependent solution of the electrodiffusion equations. Since these equations written in spheroidal coordinates do not separate, no theoretical results exist for the low-frequency dielectric properties of suspensions of spheroidal particles. in order to sidestep this problem, we used another method which relates the dielectric properties to the energy stored in the system (Grosse, C., Ferroelectrics 86, 171 (1988)) which, at low frequencies, mainly corresponds to the Gibbs free energy associated to the field-induced electrolyte concentration changes outside the double layer (Grosse, C, and Shilov, V, N., J. Colloid Interface Sci. 193, 178 (1997)). This method permits us to calculate the static permittivity by solving a purely static problem, which makes it possible to calculate analytically the alpha-dispersion amplitude of suspensions of spheroidal particles since the electrodiffusion equations do separate in the static case. We also calculate the characteristic time of the cu-dispersion from the dispersion amplitude and the static and high-frequency values of the dipolar coefficient, The analytical results obtained are presented and discussed for both prolate and oblate geometries, and for parallel, perpendicular, and random orientations of the particles with respect to the applied field.