The kinematics of a self‐pinched neutralized relativistic stream is developed in the limit of oscillations whose frequency in the rest frame of the beam is low compared to the betatron frequency of oscillation of the particles of the beam. It is shown that in this limit the beam is able to displace itself more or less rigidly giving rise to the possibility of kink‐type instabilities depending on its coupling with the external medium. In particular, the case where the beam passes through a low conductivity plasma is considered here. In this case there is a viscous drag when the beam displaces and pulls its magnetic field through the resistive plasma. This leads to an instability of the beam.