  We study evolution of a hierarchical four-body (2+2) system composed by a
pair of mass-transferring white dwarf binaries. Applying a simplified model
around the synchronous state of two inner orbital periods, we newly find that
the four body system could settle down to a limit cycle with a small period
gap. The period gap generates an amplitude variation of emitted gravitational
waves, as a beat effect. Depending on model parameters, the beat period could
be 1-10 yr and a large amplitude variation might be observed by space
gravitational-wave detectors.
