We study the formation and dynamics of normal domains in Rutherford-type superconducting cables. We use an effective circuit model to account for the electric current redistribution process between the multifilamentary strands in the presence of a normal zone. We obtain and integrate numerically the diffusion equations for the temperature and the current-density distributions in the cable. Our simulations show the formation of stable normal domains propagating along the cable. We derive an analytical expression for the threshold current I-d above which the propagating normal domains exist. (C) 1995 American Institute of Physics.