The white dwarf in AM Her systems is strongly magnetic and keeps in synchronous rotation with the orbit by magnetic coupling to the secondary star. As the latter evolves through mass loss to a cool, degenerate brown dwarf it can no longer sustain its own magnetic field and coupling is lost. Angular momentum accreted then spins up the white dwarf and the system no longer appears as an AM Her system. Possible consequences are run-away mass transfer and mass ejection from the system. Some of the unusual cataclysmic variable systems at low orbital periods may be the outcome of this evolution.