This theoretical paper deals with the low frequency permittivity (&egr;) of a dilute suspension (conductivity &sgr;, volume concentration &rgr;), in a conducting medium (conductivity &sgr;s, permittivity &egr;s), of ellipsoidal particles (major axis 2a) each composed of a conducting core covered with a nonconducting surface membrane (thicknesst, permittivity &egr;m). The quantity[&egr;−(&sgr;/&sgr;s)&egr;s]/(&rgr;a&egr;m/t)is expressed in terms of Weierstrass' elliptic functions of the axial ratios, for parallel and random arrangement of the ellipsoidal axis. A table of its numerical values is given.