When subjected to alternating electric fields in the frequency range 10(2)-10(8) Hz, giant lipid vesicles attain oblate, prolate, and spherical shapes and undergo morphological transitions between these shapes as one varies the field frequency and/or the conductivities lambda(in) and lambda(ex) of the aqueous solution inside and outside the vesicles. Four different transitions are observed with characteristic frequencies that depend primarily on the conductivity ratio lambda(in)/lambda(ex). The theoretical models that have been described in the literature are not able to describe all of these morphological transitions.