  In recent years there has been much interest in the nature of two stars, V407
Vul and RXJ0806+1527, which are widely thought to be binary white dwarfs of
very short orbital period, 570 and 321 seconds respectively. As such they
should be strong sources of gravitational waves and possible ancestors of the
accreting AM CVn stars. Monitoring at X-ray and optical wavelengths has
established that the period of each star is decreasing, at rates compatible
with that expected from gravitational radiation. This has been taken to support
the ``unipolar inductor'' model in which the white dwarfs are detached and the
X-rays produced by the dissipation of magnetically-induced electric currents.
In this paper we show that this interpretation is incorrect because it ignores
associated torques which transfer angular momentum between the spin of the
magnetic white dwarf and the orbit. We show that this torque is 10^5 times
larger than the GR term in the case of V407 Vul, and 10 times larger for
RXJ0806+1527. For V407 Vul, the unipolar inductor model can only survive if the
white dwarf spins 100 times faster than the orbit. Since this could only come
about through accretion, the validity of the unipolar inductor appears
questionable for this star. We also consider whether accretion models can fit
the observed spin-up, concluding that they can, provided that a mechanism
exists for driving the mass transfer rate away from its equilibrium value.
