2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/14175We suggest, that the magnetic field of the white dwarf in AM Her systems loses coupling to the secondary star when the latter becomes non-magnetic at the transition from a late main sequence star to a cool degenerate brown dwarf. This leads to spin-up of the primary white dwarf. After synchronous rotation is lost the systems do not appear as AM Her stars anymore. We discuss the further evolution of such systems.accepted for publication in A&A lettersAstrophysicstext