Persistent currents in superconducting accelerator magnets are caused by the magnetization of the superconducting filaments in the field of the magnet itself. The magnetized filaments create additional field distortions that can have an important effect on the beam dynamics. During the initial operation of the Tevatron as a colliding beam accelerator, the chromaticities at the injection energy were found to be time‐dependent, leading to instabilities and particle loss during injection and at the start of acceleration. Laboratory measurements on single Tevatron dipoles indicated that these effects were due to time‐dependent, persistent‐current phenomena. Using additional laboratory measurements and beam observations, we have developed a set of procedures to compensate the time‐dependent chromaticities due to persistent currents. Application of these procedures has eliminated all problems caused by time‐dependent, persistent‐current effects. We will discuss the general problem of persistent‐current distortions in superconducting accelerators, as well as the laboratory measurements, beam observations, and successful implementation of the correction schemes. While these procedures have worked well, they do have limitations that will be discussed, as will possible future improvements and implications for future projects. © 1995American Institute of Physics