The Leggett equations for the spin dynamics of superfluid 3He give a good description of the whole range of NMR phenomena observed at relatively high temperatures. However these equations assume that the orbital angular momentum of the condensate may only change on timescales much longer than the spin precession period. At the lowest achievable temperatures, the orbital viscosity of the B-phase of superfluid 3He becomes vanishingly small, giving rise to the possibility of rapid orbital motion. We have reformulated Leggett’s equations for the B-phase to allow for fast orbital dynamics in the absence of dissipation. The resulting non-linear equations of motion couple spin and orbital degrees of freedom resulting in qualitatively new phenomena. In particular, they allow for phase-locked precession of the spin and orbital angular momentum around an applied magnetic field. The coupled spin-orbit dynamics may eventually explain the exotic ultra long-lived NMR signals found at the lowest temperatures in 3He–B.