The decay of quasi-persistent circulating currents in the dissipationless quantum Hall regime has been observed. The currents induced by a time-varying magnetic field flow within a two-dimensional electron system (2DES) embedded in a GaAs–(Al,Ga)As heterojunction. The associated magnetic moment is measured using a highly sensitive magnetometer. The currents are observed to continue circulating for many hours after the magnetic field sweep is stopped indicating a very low sheet resistivity. Two distinct current decay regimes are observed, consisting of an initial exponential decay lasting a few tens of seconds followed by a much slower power-law decay. The presence of the fast initial decay, during which the current falls typically to half of its original value, indicates that the system is initially quite dissipative because the quantum Hall effect (QHE) has broken down due to the large induced current. As the current decays, the quasi-dissipationless QHE state recovers, resulting in the much slower decay, which the data suggest will persist for at least several days, much longer than has previously been suggested. The power-law form of the long decay suggests multiple relaxation paths for the system to return to equilibrium, each having a different characteristic time constant. This can equivalently be thought of as a resistivity which gradually falls with current.