Unexpected periodic variations of the magnetic field were recently found along the axes of superconducting accelerator magnets. This modulation, which reduces the field quality of the magnets, shows a complex space and time dependence containing very long time constants. We show in this article that the variation of the field ratedB/dtalong the length of a superconducting cable induces superposed coupling currents which flow over a long length. The space and time dependence of these ‘‘supercurrents’’ for a two‐wire cable model is obtained by the solution of the diffusion equation with the diffusivity given by the cable parameters. The existence of supercurrents explains the observed effects in accelerator magnets. It is furthermore shown that supercurrents can lead to a highly inhomogeneous current distribution over the cable cross section and to additional coupling losses, even in sections of the magnet wheredB/dt=0. Both these effects can reduce the stability of magnets, which may explain the ramp rate limitation found in accelerator magnets as well as in large magnets for fusion research. ©1995 American Institute of Physics.