[en] The magnetic field induced in the secondary by an asynchronous magnetized primary in an AM Herculis-type binary system is calculated. The resulting dissipation in the secondary leads to a spin down of the primary star towards synchronism with the orbit. It is found that as long as mass transfer is occurring exact synchronism cannot be achieved. At best the primary approaches a stable equilibrium state in which it rotates slowly relative to the orbit. This qualitative picture is independent of the magnetic diffusivity. (author)