  We predict the phenomenon of antiferroelectric resonance (AFER), in which an
ac electric field causes magnetic ions located at noncentrosymmetric positions
in a multi-sublattice magnet to undergo magnetic transitions corresponding to
exchange collective excitations of the system. We construct a theory of such
resonances, and show that in magnets with collinear magnetic structures AFER is
caused by relativistic and exchange-relativistic magnetoelectric interactions,
while in the noncollinear magnets a significant contribution can also come from
the exchange magnetoelectric interaction. We predict an exchange enhancement of
the resonance by exchange modes, and discuss the role of AFER in causing
resonant enhancement of magnetooptical phenomena. The main results of our
theory are illustrated with the four-sublattice rhombohedral antiferromagnets
{\alpha}-Fe_2O_3 and Cr_2O_3, as examples.
