The stability of spherical vesicles in alternating (ac) electric fields is studied theoretically for asymmetric conductivity conditions across their membranes. The vesicle deformation is obtained from a balance between the curvature elastic energies and the work done by the Maxwell stresses. The present theory describes and clarifies the mechanisms for the four types of morphological transitions observed experimentally on vesicles exposed to ac fields in the frequency range from 500 to 2 x 10(7) Hz. The displacement currents across the membranes redirect the electric fields toward the membrane normal to accumulate electric charges by the Maxwell-Wagner mechanism. These accumulated electric charges provide the underlying molecular mechanism for the morphological transitions of vesicles as observed on the micrometer scale.