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The paper is studying the dynamics of twisted vortex bundles, which weredetected in experimental investigations of superfluid turbulence in superfluid3He-B. The analysis shows that a linear torsion oscillation of a vortex bundleis a particular case of the slow vortex mode related with the inertial wave,which was already investigated in the past in connection with observation ofthe Tkachenko waves in superfluid 4He and the experiments on the slow vortexrelaxation in superfluid 3He-B. The paper addresses also a twisted vortexbundle terminating at a lateral wall of a container starting from theelementary case when the bundle reduces to a single vortex. The theoryconsiders the laminar regime of the vortex-bundle evolution and investigatesthe Glaberson-Johnson-Ostermeier instability of the laminar regime, which is aprecursor for the transition to the turbulent regime at strong twist of thebundle. The propagation and the rotation velocities of the vortex front (thesegment of the vortex bundle diverging to the wall) can be found from theequations of balance for the linear and the angular momenta, and the energy. Itis demonstrated that the vortex front can move with finite velocity even in theabsence of mutual friction (the T = 0 limit). The theory is compared withexperimental results on vortex-front propagation in superfluid 3He-B.

Dynamics of twisted vortex bundles and laminar propagation of the vortex front