  Some quadruple star systems in the hierarchical 2+2 configuration exhibit
orbit-orbit resonances between the two compact binaries. We show that the most
important resonances occur at period ratios of 1:1, 3:2 and 2:1. We describe
the conditions required for capture and show that they can be satisfied at the
3:2 and 2:1 resonances in binaries that migrate significantly in semimajor axis
after circularization, probably through magnetic braking or gravitational
radiation.
