In static and low-frequency electric fields, colloidal particles in suspension tend to associate into `strings' or `pearl chains' along the field lines. A phenomenon has been observed in which, under long duration alternating electric fields, colloidal particles in aqueous or conducting media exhibit an electrodynamic instability in which they gather into high concentration `bands' which run essentially perpendicular to the applied field vector. A detailed study is catalogued herein for aqueous suspensions of the discotic mineral kaolinite. A theory has been developed, which embraces the `pearl chain' and `band' formations, demonstrating that one can be formed from the other with increasing frequency and field strength and illustrating the dependence of band formation on electrophoretic mobility as observed in related electro-optical experiments. The value of the phenomenon as a mechanism for concentrating dispersed colloidal particles into regions of very high local density is apparent.