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AM CVn systems are binary star systems with orbital periods less than 70 minutes in which a white dwarf accretes matter from a companion star, which must be either a stripped helium burning star, or a white dwarf of lower mass than the accretor. Here, we present the discoveries of two of these systems in which there is mass transfer from the lighter white dwarf or helium star onto a strongly magnetized heavier white dwarf. These represent the first clear example of magnetized accretion in ultracompact binaries. These systems, along with similar systems that are slightly more widely separated, and that have not started to transfer mass yet, are expected to be the primary source of gravitational waves to be detected by space-based gravitational wave observatories. The presence of strong magnetic fields can substantially affect both the evolution of the binaries, and also the particular wave forms of the gravitational waves themselves, and understanding these magnetic effects is vital for understanding what to expect from the Laser Interferometer Space Antenna.


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