We show that, as a consequence of the fact that the Bogoliubov transformation mixes spin waves on different sublattices, the phenomenological Loudon Hamiltonian describing the two spin-wave absorption in rutile antiferromagnets also predicts a linear Stark effect on the two spin-wave line in these materials in the presence of dc electric fields. We present calculated line shapes for ir absorption in a dc field. The dc field needed to observe significant effects is of order 106 V/cm. The Stark-effect experiment could be used to measure the parameter of the Loudon Hamiltonian, which is of interest from a theoretical point of view, since some mechanisms of two spin-wave absorption predict π2=0. The Stark effect also provides the possibility in principle of producing a phase transition in these antiferromagnets by the application of a dc electric field. This is the case because the shift in the spin-wave energy produced by the dc field can be negative for some values of k. We study this possibility in a simple approximation. The required fields are too large to be realizable in rutile antiferromagnets but there is some hope of observing such transitions in other kinds of antiferromagnets.